%!PS-Adobe-2.0
%%Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software
%%Title: ode.dvi
%%Pages: 24
%%PageOrder: Ascend
%%BoundingBox: 0 0 596 842
%%DocumentFonts: CMR17 CMR12 CMSY8 CMTI9 CMR10 CMBX10 CMTI10 CMBX12
%%+ CMSY10 CMMI10 CMR8 CMMI8 CMR6 CMSY6 CMR9 MSBM10 CMEX10 CMMI6 MSBM7
%%+ CMSY7 CMR7
%%EndComments
%DVIPSWebPage: (www.radicaleye.com)
%DVIPSCommandLine: dvips ode.dvi -o
%DVIPSParameters: dpi=600, compressed
%DVIPSSource:  TeX output 2009.11.04:1719
%%BeginProcSet: texc.pro
%!
/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S
N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72
mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0
0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{
landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize
mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[
matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round
exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{
statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0]
N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin
/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array
/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2
array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N
df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A
definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get
}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub}
B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr
1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3
1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx
0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx
sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{
rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp
gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B
/chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{
/cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{
A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy
get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse}
ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp
fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17
{2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add
chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{
1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop}
forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn
/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put
}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{
bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A
mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{
SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{
userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X
1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4
index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N
/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{
/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)
(LaserWriter 16/600)]{A length product length le{A length product exch 0
exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse
end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask
grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot}
imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round
exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto
fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p
delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}
B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{
p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S
rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end

%%EndProcSet
%%BeginProcSet: f7b6d320.enc
% Thomas Esser, Dec 2002. public domain
%
% Encoding for:
%     cmb10 cmbx10 cmbx12 cmbx5 cmbx6 cmbx7 cmbx8 cmbx9 cmbxsl10
%     cmdunh10 cmr10 cmr12 cmr17cmr6 cmr7 cmr8 cmr9 cmsl10 cmsl12 cmsl8
%     cmsl9 cmss10cmss12 cmss17 cmss8 cmss9 cmssbx10 cmssdc10 cmssi10
%     cmssi12 cmssi17 cmssi8cmssi9 cmssq8 cmssqi8 cmvtt10
%
/TeXf7b6d320Encoding [
/Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega
/ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute /caron /breve
/macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash
/suppress /exclam /quotedblright /numbersign /dollar /percent /ampersand
/quoteright /parenleft /parenright /asterisk /plus /comma /hyphen
/period /slash /zero /one /two /three /four /five /six /seven /eight
/nine /colon /semicolon /exclamdown /equal /questiondown /question /at
/A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X
/Y /Z /bracketleft /quotedblleft /bracketright /circumflex /dotaccent
/quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u
/v /w /x /y /z /endash /emdash /hungarumlaut /tilde /dieresis /suppress
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space
/Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef
/.notdef /Omega /ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute
/caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE
/OE /Oslash /suppress /dieresis /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
] def

%%EndProcSet
%%BeginProcSet: bbad153f.enc
% Thomas Esser, Dec 2002. public domain
%
% Encoding for:
%     cmsy10 cmsy5 cmsy6 cmsy7 cmsy8 cmsy9
%
/TeXbbad153fEncoding [
/minus /periodcentered /multiply /asteriskmath /divide /diamondmath
/plusminus /minusplus /circleplus /circleminus /circlemultiply
/circledivide /circledot /circlecopyrt /openbullet /bullet
/equivasymptotic /equivalence /reflexsubset /reflexsuperset /lessequal
/greaterequal /precedesequal /followsequal /similar /approxequal
/propersubset /propersuperset /lessmuch /greatermuch /precedes /follows
/arrowleft /arrowright /arrowup /arrowdown /arrowboth /arrownortheast
/arrowsoutheast /similarequal /arrowdblleft /arrowdblright /arrowdblup
/arrowdbldown /arrowdblboth /arrownorthwest /arrowsouthwest /proportional
/prime /infinity /element /owner /triangle /triangleinv /negationslash
/mapsto /universal /existential /logicalnot /emptyset /Rfractur /Ifractur
/latticetop /perpendicular /aleph /A /B /C /D /E /F /G /H /I /J /K
/L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /union /intersection
/unionmulti /logicaland /logicalor /turnstileleft /turnstileright
/floorleft /floorright /ceilingleft /ceilingright /braceleft /braceright
/angbracketleft /angbracketright /bar /bardbl /arrowbothv /arrowdblbothv
/backslash /wreathproduct /radical /coproduct /nabla /integral
/unionsq /intersectionsq /subsetsqequal /supersetsqequal /section
/dagger /daggerdbl /paragraph /club /diamond /heart /spade /arrowleft
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/minus /periodcentered /multiply /asteriskmath /divide /diamondmath
/plusminus /minusplus /circleplus /circleminus /.notdef /.notdef
/circlemultiply /circledivide /circledot /circlecopyrt /openbullet
/bullet /equivasymptotic /equivalence /reflexsubset /reflexsuperset
/lessequal /greaterequal /precedesequal /followsequal /similar
/approxequal /propersubset /propersuperset /lessmuch /greatermuch
/precedes /follows /arrowleft /spade /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
] def

%%EndProcSet
%%BeginProcSet: 74afc74c.enc
% Thomas Esser, Dec 2002. public domain
%
% Encoding for:
%     cmbxti10 cmff10 cmfi10 cmfib8 cmti10 cmti12 cmti7 cmti8cmti9 cmu10
%
/TeX74afc74cEncoding [
/Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega
/ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute /caron /breve
/macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash
/suppress /exclam /quotedblright /numbersign /sterling /percent
/ampersand /quoteright /parenleft /parenright /asterisk /plus /comma
/hyphen /period /slash /zero /one /two /three /four /five /six /seven
/eight /nine /colon /semicolon /exclamdown /equal /questiondown /question
/at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W
/X /Y /Z /bracketleft /quotedblleft /bracketright /circumflex /dotaccent
/quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u
/v /w /x /y /z /endash /emdash /hungarumlaut /tilde /dieresis /suppress
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space
/Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef
/.notdef /Omega /ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute
/caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE
/OE /Oslash /suppress /dieresis /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
] def

%%EndProcSet
%%BeginProcSet: aae443f0.enc
% Thomas Esser, Dec 2002. public domain
%
% Encoding for:
%     cmmi10 cmmi12 cmmi5 cmmi6 cmmi7 cmmi8 cmmi9 cmmib10
%
/TeXaae443f0Encoding [
/Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega
/alpha /beta /gamma /delta /epsilon1 /zeta /eta /theta /iota /kappa
/lambda /mu /nu /xi /pi /rho /sigma /tau /upsilon /phi /chi /psi
/omega /epsilon /theta1 /pi1 /rho1 /sigma1 /phi1 /arrowlefttophalf
/arrowleftbothalf /arrowrighttophalf /arrowrightbothalf /arrowhookleft
/arrowhookright /triangleright /triangleleft /zerooldstyle /oneoldstyle
/twooldstyle /threeoldstyle /fouroldstyle /fiveoldstyle /sixoldstyle
/sevenoldstyle /eightoldstyle /nineoldstyle /period /comma /less /slash
/greater /star /partialdiff /A /B /C /D /E /F /G /H /I /J /K /L /M /N
/O /P /Q /R /S /T /U /V /W /X /Y /Z /flat /natural /sharp /slurbelow
/slurabove /lscript /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p
/q /r /s /t /u /v /w /x /y /z /dotlessi /dotlessj /weierstrass /vector
/tie /psi /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/space /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi
/.notdef /.notdef /Omega /alpha /beta /gamma /delta /epsilon1 /zeta /eta
/theta /iota /kappa /lambda /mu /nu /xi /pi /rho /sigma /tau /upsilon
/phi /chi /psi /tie /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef
] def

%%EndProcSet
%%BeginProcSet: texps.pro
%!
TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2
index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll
exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]FontType 0
ne{/Metrics exch def dict begin Encoding{exch dup type/integertype ne{
pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get
div def}ifelse}forall Metrics/Metrics currentdict end def}{{1 index type
/nametype eq{exit}if exch pop}loop}ifelse[2 index currentdict end
definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{dup
sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll
mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[
exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}if}
forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}def
end

%%EndProcSet
%%BeginFont: CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
/UniqueID 5000790 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMSY7
%!PS-AdobeFont-1.1: CMSY7 1.0
%%CreationDate: 1991 Aug 15 07:21:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-15 -951 1252 782}readonly def
/UniqueID 5000817 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964
7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4
A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85
E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A
221A37D9A807DD01161779DDE7D251491EBF65A98C9FE2B1CF8D725A70281949
8F4AFFE638BBA6B12386C7F32BA350D62EA218D5B24EE612C2C20F43CD3BFD0D
F02B185B692D7B27BEC7290EEFDCF92F95DDEB507068DE0B0B0351E3ECB8E443
E611BE0A41A1F8C89C3BC16B352C3443AB6F665EAC5E0CC4229DECFC58E15765
424C919C273E7FA240BE7B2E951AB789D127625BBCB7033E005050EB2E12B1C8
E5F3AD1F44A71957AD2CC53D917BFD09235601155886EE36D0C3DD6E7AA2EF9C
C402C77FF1549E609A711FC3C211E64E8F263D60A57E9F2B47E3480B978AAF63
868AEA25DA3D5413467B76D2F02F8097D2841EDA6677731A6ACFEC0BABF1016A
089B2D24F83F8FEECD9B11A16D76AD6AD0934A8604FAE813A1304C950E76FC3E
D0FA05FBAAD62B378AC5316425609AD3143A59FAAEE73055752EBCB7B784017D
10D7B44D7DF4D4793D776B70373076A662D812E29520E2915F7D742EC0650CB3
31FDD62F15E4D5BD0CC19D2E1C7364BCEE117028BAE01859A6AB353634EBC37C
ADDEB23C853A9AA732CFDC99134B91D9CE53E3E9C3ED2CF043D4D2E985346C98
DAD4A3F598E68E5DE482B93DFD55D2705D05D0D4B14B288D72B73C2E1B2543A2
E18C363CD7BF6FB59AB75C0BDB66F9FED7CBFA62042FAD21C7D592FB1D2B3A6C
4643296A34B1C67E11D1D1D988C1415A4AFBD1A32802F05DA5EDE57C6829DBD8
87A5FC79B176DCC55594ED46FE588E7D6BAF902B8231695ABBFDEA733923B39A
0671D24103DC517C1FE0E93FA71E36B9F5327D83C5093C1D3054810933524C4E
FEF311EC5CA6AF0B83316B093DD08F295D
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE
3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B
532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470
B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B
986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE
D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958
9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321
990CD249827D9648574955F61BAAA11263A91B6C3D47A5190165B0C25ABF6D3E
6EC187E4B05182126BB0D0323D943170B795255260F9FD25F2248D04F45DFBFB
DEF7FF8B19BFEF637B210018AE02572B389B3F76282BEB29CC301905D388C721
59616893E774413F48DE0B408BC66DCE3FE17CB9F84D205839D58014D6A88823
D9320AE93AF96D97A02C4D5A2BB2B8C7925C4578003959C46E3CE1A2F0EAC4BF
8B9B325E46435BDE60BC54D72BC8ACB5C0A34413AC87045DC7B84646A324B808
6FD8E34217213E131C3B1510415CE45420688ED9C1D27890EC68BD7C1235FAF9
1DAB3A369DD2FC3BE5CF9655C7B7EDA7361D7E05E5831B6B8E2EEC542A7B38EE
03BE4BAC6079D038ACB3C7C916279764547C2D51976BABA94BA9866D79F13909
95AA39B0F03103A07CBDF441B8C5669F729020AF284B7FF52A29C6255FCAACF1
74109050FBA2602E72593FBCBFC26E726EE4AEF97B7632BC4F5F353B5C67FED2
3EA752A4A57B8F7FEFF1D7341D895F0A3A0BE1D8E3391970457A967EFF84F6D8
47750B1145B8CC5BD96EE7AA99DDC9E06939E383BDA41175233D58AD263EBF19
AFC27E4A7E07D09FB08355F6EA74E530B0743143F2A871732D62D80F35B19FD2
C7FDF08105847F13D50934419AC647CBA71DF74F4531DC02BBDA22AEEA3FBBBB
407E0ACC52BDC60D01A29407CC4F93EB8BF6D4813E9BA858D54F38918AC82720
4956D50291F0546E50FCAFA6DBD0099123F5ECD4AB338DB310DB4CAE11337A89
8ED99B6F483940C97544F888EAF0CBEB11094A13C073D0061808662A04A82BA0
AD35E8782F854AF66C20C0FEF18D0ECDD1646321B93D327E53D88CA0E825FA95
05AA57BD7ADF60B2EEE99B3F4D56D706E3C0B1B1ED3328CBC4D870ED645E4CA5
53B513A2EE1608D3EC72B25D2F7501A37CDC73499020C15F1A3173BBBA7BCDAF
9C16998EF7A5805AEA49B86A8D0B621486FE6065AFF9FB2AECB6740B11B809B9
30426AA08B05C8280B08F0ECF83019EB2F853AD4455104E3EA1EA5A0890F18A0
CA618CAAFE0B63C9972933FB27A3DD25B740EEBDA3DD85B64E7B5E8DA7068999
75622908A2AFD77F47ED35E027D0E8CCBEF11E3AE56B715F6C88F0C724792BF9
F6AF95892A45DCA0BBCE9640C821039DBD1F0FD90EC5C6048D5F63851A59734C
F516A9CA4B2A29E78D1F931234B4EFF8053527037216F0BEF23359D462FEC95E
C0BB431847220F107126D18064456767015F661B78B0295C954B21255EFC994C
C21E2C22AE5D2BFA431AC0225150BCF15CDA7F59C08431FAEDFFDE0F5FCF11C3
3CE6AE7911C3C5B6E528CEBAA1D3B084EC6FCA880A1EB76A6ADE85EA193DD3DE
8BF4EE4D29A7D0DE24FEC1F6AFF00CC2F0650368B9B6E4A307894782C66AA0FD
854FB296575F08692CDA940DFABD5A540B7DA7555B8F30EA79A256831BB45F78
74E070EA453D3AB918DCA937A696DC1C1D34AA6645D2939693A3E43F25BB5BD7
816D604C057924DAEDA1D71B86EC594111A7EDD0C0106E7F182F8EA538A107B6
988431231D2B86B324FA9AF2A162583DF5E84DED99BE9109E353D6F5562D9BD6
488FD3725C1F328F995598201E71CD45922DA884F39F8DC4F40432A8F3455092
68C0A484BF0F311B3B58190EAF347CC996ED78B5BF1500D4C0680BE8277D6FD4
5EF218F7B37D1A08A1BE03D638F3AFC7E27640D6AEB7AD908781C83C4E111EE0
07C88C89FD8252EE9AF4E577C083D779B3B1550854E7E5A9C5EA773DC0172DAF
5267F5C64E1BB7B8FEF196C053BA0E3B73E5A5478B1C13C1DC53866889C48F14
ADE0992EE2B310B1E3665DBD3424DD52EE75B6C0DDDF76CFC8D658FC4F0F8119
1C16AEF36FBB0692D344A70C9EDC9D931C52B433B4524C60AC39F32250A34ACB
3CF84C7C36CEC7632AF43E2D29126A40BC2F113867AEB5719F351B5F69D243D4
9B3CDDB702A1E39AD24E7944E13E5F8CFCB7C5B859047230AA557A8899F15710
83A06C55AB49A67ECD1AA409005707B970EE71625218BBC43509C649697FFC19
9A192B7540340FA4DAA9F5BE90729F4C6A99043E7EF487DE78AA74C29987C39A
AF8801E850068A7AC0036A9541D9C9644AE61FEB480BE0657DF735F57621470B
BEBADED402700B0A6056B5986CB033C7B80F20A63C1F5EAA7C9422C92BCA7FAB
6C49D4D723F6D6238D4F5CAFE2A723B13C5CF09DF6A08ECC7CE5FB29D9486073
73F4051AF07FCFAC87E118CC0747ADA1FB9C7C96B76FA6304E4D9EBE55E7F36B
822F48F5FEB8341778B6ABF10786EBDB32ECDC39CC0C009447632C6711839A27
0A1E5C068D88C6F8C86D63EEA94B52F0AD3D40443B3A8A250BFA442F70801878
8A4A714DAA2A02C4B1999F66DEE4C919DB1D10D0F1E6283F546E5E1D49B8FEE9
F008DEA3D4578140BC3BAE7112D8B48BB638B729A6144181CACE0829A31368DE
5D00DE9F3967664220978D6FBD00238C33859CA5D89191ADEA0C66B851C10CEC
4BFB44072A40854A39F532C8E4BC94E9E729259AA51D34A10F107DC3B96096E1
D7C0B92E93E70356A2FAE6600DB1C5940CE6411FCE1A727F516F22A848198655
D1579A37A541EC9EC1E27A0165BC2A2AD1F687F8E1B098335873D7B5DD4C08F9
33DDF6A2F07ACE5B28DC085664B93361EBF3FD197569BF6159D6E0E2A6AEF411
92D352E2A4F3DCB7B3097D68106912DC4AD9A338DD16D7E2BA8E3D8A153D7F9E
E3795693CE44CEFA61BBD27F0C8ED3D45A733BA6AD7FEC2D3A8D006AAA6AE03C
A4BECBBECD0F8B636EECA74C254BC9CEBD31E91AC716E6E29ED36A4D475C611B
5977B92ECBE5B7FE7D1CAA7E12DE4F0A32C65E3088645F89A7ED20811881E9D3
FE5CF88A0DD00F783F01F6602C7F4BF82825114FD389B6DC61C8924283C867F9
66E0FA193238C6ED0EE2C13475EEBBDDED3A0608537AD3849C5AE4AAEA8090DD
792F136C3012C6CC7D783373B20E2FC3B26EFACEDEFF6318EAAF62D082A59539
CB80D75EB7802DA9FA674A12982D0032B0C93093E210B9EBA7FC82FE13E70277
828C03C47AEF07A3AA8070029EA48F5114BA7A859C7F96FCD866BB0740D7A736
8FD2F67AA5D9C7709E7F1DCE107B51127923FC0228A278D74ABA7D756C4ADB73
8491255CC72AE9FECC3D0A4FB398785E3362AF155DDF9899D64632F55FBA1B81
5864F4F4945D1C3F0CCBF598915F7765829FAAFF4ECDC9DE18BCCA0AE3CA4375
61080D607D4432D71F8F77195FEB63C149F09BF58A06DC6079F118CC1B670A6B
302670CD6838F2EE23768042DEF571A379631E08A5A5C8762B498430E05B50DC
503CDB70EB778DD7B8E2D40B1CE7EA4A6EA684E3408A54B27B4C41A9ADB9905B
8A0D34B3422CBF0C82D80DDDA15DB29D5F8728CDCE8B960CB9F103D0C64A6093
4E6BB17C12C26B2CD05154BE6C69C0DD762E60D6BA28FAE0732C574BF2A87967
9F57B0DDEBBCC9034D6127045CC1E5B7A4F0295DFB1BDE471B191D32EB94A835
BBE67D31120599EBB2344208EBCC89333AEE30239946AA40B1E9E27A8D989D35
D8801A26DFA530BB18D57D80AD9F7A19C16E9607DA84AC30A84B78FF1973056C
0A8A322385C9CAB3EDDFE79403790AA4FBBA743FCB1334B301C2F2C773064130
9EC551D0ABA8CDA1F0E1E314E7C0B881C7C27DA7B74E7520F39D3B0FB495C08E
E7C8FBED44853BD66EC8FFD2443FE3AEF472E059488ECA4F1E50AE409D0387DA
2AA998CC1FEC4E4B863245DC74A2678F829FBDFFCE54F11FAF695088E2D8F171
B6C2A64D403CC382BF92AA782B543B9B965FF7EBC57F157AF10D17C2BE7254A9
6724A22B38506ED41BDDD0D99B444354379416A22F9EF55964147AD9123D7B59
C0252FBC218A445280C4F45CA7057DEC878D5577EB0CC6C7E29246880B661117
A3227E12B8F07FC337FDF3135B207DE174DCC5B2926AC1EDFFFBFA83FDB89A72
6CE9C18A5E49CC695453B727B00CA413199B08F3E69AFEB2D5B8F03D448730B2
110CBF5F566C0E4B4E47BFF9501BF396B09BB5AC76D81E4257E5842590667A0E
9E83704CDE1E002088C47BA9019F5D878078B362C348D065838725903A3046B0
054189FFC43C97F9035626F238F1EB9825A3E0AEF359BE61CDD0E6C6C4F563C5
6A541519936026B74D576BC837AFD1FF299A15E1A51BC1E31C8A5CB0DB667A9E
E8F0085E1A32AC2753150B187FBBA341E85F70E257D2781572D82A3C082A58AF
A316C4665CEDFE39E6B6BD508C100E3919B4C836B857FA51CDCEBC17BD03FBD9
C1F103681BF59321F5AC20E1B624E7531002D2AF2111B94A667C7D601E950AEE
F4863BCE7C8E16D9204A7F23A41022C360D5DE7228471DDBFC75C1CFB3F5705D
CAF2EF9CC2F40ECB262148FABE2BFC5223B18CC94035E4A377B49762E6542EB9
64BA6836BB66606F1DE3B8B4E83FAE741B45BF2BC4BD9FD070E798D820211477
C7B8F260A338BA325DBBE6C21A28FCDE85732943E330473946E6E8C9561095A0
CBBA171E4E48C2E95B0319165B91FFC52FAA7499C5DF72888394D9A5EA88184C
7E0DC8D93961F95919906EE03880E04087328575E5DB609C6958899F8280ABC3
BF59B9AF0BD7C15CA436ACB9F2CDDDFF6631C7C1F0CD1255DA113F45E0687BA1
2F1B24DA8543230CDC8414AB2EC4BEC68A2FDA90C920F6871C8ACB1ECA2C1C46
1B1823E682D043934F78912086DD8CAAF3F47B3082FB61090F2D007AF8334885
EDB67D88181342661879F4E7AAF7DE8250C141F3997900255491CD73709C6CE4
DC235645E37AF644BC1080A6FA91A116A7E824465EF5E9C8A86B8839EC13C25D
ADCF415C70B8E33C9CBBC353E982ECF69C89EC4E7AA3E9726BEABDD96E2E1F6F
B5E11AD15ADA0068215E020F6EB22BD7DAB31392CBF1FFA752B628BDDB859A12
6F8712FB9A1747FF229A3F208A36418A954FFC111C070D3E7D34614549F7B0E6
AD2A33692E1E352FE8755BD87C0E9B3DB0D3E011FEE488D34E8807255FA1B90A
B7A623CF7977A7CD16E30BA655FFA98CAD7F2A56B2A49604637BC96AB6F0B5FC
B88D67FC0C89C5E0973FF83D452E05933DBC6BFAA3C7ABF4B6AE69EC1C22F391
AE85071D48E751CF6FE26720A878B2A8F593BF75DE5002A40F1675070EB49DCD
FC55B10D7C79293BF4A7BA0CFCD2954027FAE485EC19DB61A56778023D7E38EF
65C6F9B6862FE9C59E1FBB80E9C94F1D81ABD338FC4D801A06F763FA088FDCBE
A52184BF2040E9D138F2DD5E03276D1F2D2C16208402B12DE1D06D026815706D
DBBD562AC9389A6D565C4858ECEA63221DCC8635CB497AB409B30E8393E54D6B
059D5FAD511633F85DBACA13D1E520508AC0EADF83A98C24E4F4440967BD5586
6B903A05F132ADFAAF960DAE91D29E753C16AF3FD12B3F8D64C26FF51A3B791C
D7F925A32DB978A8DBF7CC3DD1A239F789FF17AA7237665905063C649E8F6B7A
8738216CB1B769A8FA305563EF5D30C186A7AF62ADC15382D729D41F588A9E84
D70010F6565801528C85EAF257204CB983C5CB4F902F05E3E1D4A5F62377BC06
6224C72C1FB94252953E50EE2979DC5C5C6EFD000ED0DB4D99E2577E4D9FF5BB
6ACD6BE4EE208972C1FDCC73BCB554E4D5F2B97B38A493341EA72415F12E93E0
5530EC56238B1DDAC9C51AC2471E024A049F9480AD010D56B7B885A648D3DFFB
F6A7A8A855968B10F7D4881E40ADEC46B343E24310EBA6051723B575140C4BA6
2D17ED4A196859BAE935AD5136F65E07762CF4B7621A45DDBF634DE1487D2E39
59D37C75109424CCF4878E70AB9EE17B15926234689254B822EE5CDE47AD173B
73336AA5325691BCE72693EBDAF58042B72D69496F57A32E715ABDF84AB7BE70
FD6AEDF8363E197A4B541BB8218311F2FAB9C96002C75B0D16DD8BD0264B007E
F101B37558AD1663C49EE4677B01AB30151E4E0DEC6A65A33286D541AF3E9790
B7A4E136C0697A814BEAFFA1A9E9DE4291FE975940AC2F02A9EC89FF29115E7B
1F633A277BB576CDEDC597399570C7FA242550D7F6224E32792BCC4A42C3256A
1479E34F1E42DF4662178BC61AF29AD04BCAB9EA116350F8610C6D2B085CF4EB
1E0DF01DEEE676DCBEECCBE5C02064E9A5370404D1BAEF96D3E847647E37A341
3DD3DC796C1A4689D4D71916B7FC735DDD75B9738005DE0ED715A2A742A9A557
EDABBF747AEFDB4895D86102D3AC015609D8453AA5205D8C20BB57BB6B7E452F
C664DD243C521CE7A28AE8DDBD553BAF56FA7E78944C83F0A1832A39936FEB50
2560FA69C7CB0A98E3C6022C042315B17B89F78F59C5F04D1122EB1915323DB7
CF83F262A828B3D922F9CB429646771D5BF8EE4D6FB04D451E15118BAC6DC40B
1DDB35282BA05D2FF157527EE4DD6EEB2883A24174B800306D409E268F964435
FB54EC349A24D2A1AF636C2C1CCADE1FA01EE079D6B9DFB94FC5FB7F5256CD7B
D3A9D6E5994333C76169989CA35D2CA568002828EFF44FF6260006B2AE1DD8C7
B835375E5F7BF5BF3ED2375466FA6674BE86215D56C259664C4F614A79A278DE
9CF54926CFE873B00C7080A59A2215115E512FAD6030388DF0D7EA442F72ECC2
4B16BD409A69F2A3966E78DBB79F11394343880AD70A6DF397868311BF2F85F3
9BAC7573F563364C5EA7E75A46E684D9A67EF9CF9E27A695193E96CAF4226786
2ECF3C93BBE53013EFB3EA872B7A78C718B2A17AEA3AC4E355351392DBD1066B
F4B22D17C9F82D8358DF2763A71A64C3E86469CA376CE26091156613327E0D57
117CAF3F299CDBFC27AB59A085CE37D02AA302E8E89D7D10D2066F69CBE7FAD8
DD729C83BBA956A475D84C08B08C5FAB1D1E46E7B5986E715FB902184BFD0BA9
81B4B3AE825ED7F5BF36754227E9EC22C355A9B89352B36F2C83406AEE6A729F
4F11D611DB6FE0DC68D8082463796333E54A8D6D7AB3ECB1DE95C03E6CBDB369
C4FA4610E3F3BD7AE6A5C0D981BD07332F997DDF09C5415C3AE2B24DF94904A8
BD58AB5798461434E9E270EB53BD0074AF6626DB9C4341D0794D45D35909CC03
F84A0A160BFE3AE3D500FFFAE5EEF678C52AF1D6A0D852C2A375D7264BBEFB3C
96E5D34B552F027032208BFE3856E6235D2213E222D13096D2076580B939374D
B2BC2D37C6E9C41368C299B058FF61E4F9AD2C5A5E41759D954C6C0A90F9F348
43F38C34974959127FA636CAF351AEF32703B657BC53DA45C9882CE503EED359
9E0BA2A0635A7264EA3F99C8E16F78016D5B8B49909C74BE89BAD142DAF0C918
CAB3D319C03217BA2420F27327E22005609089B8D21CA70C8A2D25C42C0DE473
F88DC940AF4176EB6FE8216499E7BA07EA6F7439739D6AF20B5B8255B6D78979
06619C7C332DD546C4E73D4B78F2C6FAD6A1A6EE09E9EEDFD27F2ADDAA38944C
B693760BBDF96ABEABA90246C86BEFC6C041808353D3B3E2C08CA8358570132C
7EC4DAEA854ED80D94AAF347B74005816E4F4ECE452CF6D167E79595D7896893
5316CE12C10E408140B190DC8E9B9CE2EA13FD88EF02F41B05921532717A4952
DE23C48C48683D6320A45F3AE9C027CF9FDE99363C940A0F0796FAF292B19A8F
73EC2CEE4D69D09B94E6BBE076F1D73F6176DFA33B08F20CD7FF3B9EF9E7FA78
19C39C4A0194F1AF2401471AC74D537578FAB6C96B3159A7425A5CF82F8FBE5C
9385F24E85B12F60E2D39E84F8A1611494F2BCD7F4E0D402666503B12E71B34A
E134B1AF6E598C8E2D1BC3641DC0D0A43D7962B3447A416164C61B9529EE6AD0
CEB4CAA04153763B304FCA02BE40EC3F1C423D7AA3D4DE9E79DAA41A859692EB
252316C329FDB5540E8BA03954824A4325D1C3D2DCC4E7AB12292206BE08A8E2
83AB5E004AF64475668912E1C6A59EBD6D612D5199A23E01741835A55CFA790F
A14A162DAC3C66351EFF16D9812DBC7464D498D358F8541A6802F1D798DF8C64
EF08F4394E8CC36991A6A0F2CB3A737FA2D5FF4D4BB8DCA8F3B5B9500FAA184D
8AAA239203D5B919BF76235B64E058E746BE80FF9057335402AFD6E4833BA744
ACC5044AD103904AC97C1278EBB054C70118251304019EA141157AC6C84376A0
F7DAD30B944FDAA2E249F7828151BC23057EDCC9212DFB09903C9F5D49A8F57B
8ED70DC1D604A0FC40D2AE271E5FB8928DE44A97E7C88DE8CE9E0F0540F87F40
B83F204DEB572CDD1FDB87D157173075556A673D6BF90F324DB84FDA2DA9DF04
CB7FA1C19E846B212CE6860E9A71102E9B96600CC21D8AAD46C092067A355997
537A7841DB40A33E7DBB344710C8E74C0F62784AA68378C9639C29A2074B41FE
C990841D148C38E9CC93DC148CD97705BBC8657AAF906D1BDDBBCA35378002AE
6D5B7D2BE3D462FC199B17F8E18C7BC4DDC7C6FA1EE4968E8E0C9C069CCDF990
E860E30819E7C7BD0A2ABE4A6778D6FA7DCB782FC23F6BD6BEB37FCD636BBA0C
F9CEEDFAC3AE2D939CD86FCC212F7CC2EDCFEFD0E6BF073092244A65AC503915
2E135EA148F5D66EBE0F14947BEFBC42083E54B7B4FA572811DE9DBB35CBB5ED
2167DFEC2F75A6F0D8655F49F1E8F03FCD0FC45E495734744C27D7B8DD6059FD
66B13D6FE7855E49086C3EAE016B0FC79D28609AEC0757A1F4F83229F508D286
DE93C97F94FD03BCBBE9551B16111CBCF7847E4C2E7A41113D31047B8F588912
05D344ADBB4F4D7A1772688BF3C667D0BE5B29DB87AAB415EF54FECEADCB50E1
199BA6B0369C916E244A12EC0CDF898B97D4D3884F32D210AE1B9F97FB42BEC5
56927941C57914844A0090239F36C69860FE86658CDB11488B1EDE42DB84CF9F
027F0D3F2D5451BBB2851CDE508B7ABB45372A3B04EA5CB5F398919A64B6C666
39464F20A25BDB8F037FAFE5E052F84D9B4D83287ACB8D1E53E14B2DF2FAC3F6
1DC44F9374FE0D95AB2568B4445B2B57837BE720A7B97C5870B9BDD1A3490497
B9EB93657781A74341C939A2631878B01698443BE7E8B6736C58465A9B2672A4
21FA83143A8BAD2E8CEE36BCB784DAB1C964CF764446202DAD483AF41A88B496
62FC6168F433E58B63BBB2109DCFE9BA79DDBD97FD2850F61D332F8DEC221737
695E313502F0D96D2484BA71E4C95C19A9685B7F4F220360D500E0C89725200A
30E588D69CE8C653666B53108047948DFC77C78F0FF9D680A590D60277A4AD78
D08EE466CBBCC978E81E9E14E99B600AEC3918F6662147E875BE61F647D5897E
9FDE948BE81E03BFEC6AB18FF5A8B47F899C16773FADCC98E46A97F4D5E72A85
B9E855ACA73B96F7B23D593EF86E7BD0BA9E1F0096DFDA5EB05BB0CD7738E1D5
137F0ABE83C7E13F6214065AFB61D5E24D59E3BBBC65A21502CA1CB684ABD70E
2B35BCF80C6D85B997DA1349BDCEC78BFEE4272DDD9EEBA14C13726098DD4686
F1682DECCBA046C4F2411B7F5624AA916AFD3E99682FAA9721333D2FE1EB5D73
4DB7AD48FF9940332CB3ACC8190796EE17D9EE95B6CB44D3B774F3A45BF1570C
83784B50BBD6087F139B561B633029F9613878C60A616989AF6250FB8BCA5C96
AC2CA353BDD5C056044A24FB891508AEE84BBE57E45F17EC6DF8CBB6E3705BBD
5D33CCD33A41C4BC60A3F6A383323FA3BFFDF22B438C4CAA9817EF8A0B118864
A0F6FDBC2C170612880BCB815C0BAD859A9AD7871AA23CEB6336DD7CDA4C7D57
726E9F243CE8A0D88074690BFC6FFB1BB794D033425B54EA833078F483FB87AC
DEA7A25F4ADA822A48F68E0021DD4CA55A2E40FC84FB3415D9918815901DE610
3540DEE637FAA112BE52DACEAB52E7FF3EC1F7A63CD07B2CD68B8F8EE4ECC614
976BA0DFFCF291023AD8A59D08064BC8C1E05D82E6A6631F3F98719A0A12E9EC
505D3D37FF99F9A1750D7F0B1E455CADA8BE00E96FF905F5A2C4E98DA584C48C
A9669E3F2C03FCB8D6984CD6E271E43937A1BA7571FC2138BC61F825C8AA8390
6DF6FB85D556982BF8D69EB97ED114645018A4C2A15B4F557A4F3810E324BE6B
EABB8E602459320F5002163DC5E9040E745DC103C998EBA6F129BB2158EEACF3
0803F0510DB9EDDFE4A84CFDD01545431E94F93981B9B6D216EF577EA7CB4533
14A3C1DE3EF348E8E64B89EC689BE7B7D7B609B07B8350AFB16D4F81F420994C
C7875D4774E06F8D0375F96F466713F2EB8DDC1B50756F70D7A007BC07278B3D
D3B7B665E83A4E245454F1F89BE3960082A69D3248F651EA57C89A4816511DAA
E69DD33ED131814A60CF93EE9547BE65EF925C1645F5E454B85443ED618C460B
903A93002D8A4768644BE82BBD2F5F1B9632AE78719914AA74C807280D1C88E2
9AF6E058CF2D34CA50A5FB054222585B104430700FCF9310A6DFFABC3220091B
D310BD4B80A248A2A6E231088DCB0DD5DFD69545D3A529C216C7FC4FF9D0858C
1F99DDC8A061A5BD3561EB16FBA7542FB37A3D93C24C082D5EAAFA9224EFF5BF
B4B7264F2852FA130102E86E6E4EBF0293C3577F91BD895DAFDB6EC434E69F6A
4F0B94ECBD26CC892F6343D7CB3837AC9BDFA60BE3969127C7D071AB2FCB71CF
527427259F0166ABCD9AE7FA9FAEEBE24CC6CE2C82F11867D041F7704F75DC98
15714A4E4405B39578358D82714171163BBD7F872394A3529351628B53322C7E
4B484D85E95335B3A0EBE51E91C86A2BFCE995AB4FEAA99A39A2FFB74CEC6C7C
1D704996D6E2F4630B1DCB08FC8FC12303D3FC9AFDC523467E9431DF5CFED6AC
A366F1D5FC26CFA29BB77B1BD4221307B12A951F34F23A50DFF95FA46DD909DB
2B9B7D4E038793E78B3D1580EA415523677AEC073AE462E54AB486AC757961DD
2A93B8F057B6A0FD3CC797EB619A01757038BF6C7513245BE5FB766FBBBCCB8D
951497D790F6F664C2676BD2600583E7767B347E67A612D5F286E17C069A5FF9
393F9F1BF484ECA73365CCE591C03101AD32989DB3C49FD6649AFFD3F12EF092
D9F9FEC70296D7E19444991E4D95021F80BE6FC94AFDA52343D12D1B5B729A05
1A8A70CB7823F96DCE8D2C3DCAB853A7861D03CA7E2E4623D10DDAF1711C6B45
01C8C8A8FEC7BDE3ABB2E03258794692CD9C9DB599EED62B8C25C23B0F1FC4F1
E6E3E67FEE71ED62D2AC6D7F3C9C8DE44B6E47A995321FBEA20966719AA20549
C20DDA71BD43C4FDC8469FA4E8B2D63E9D95EEEFB6BB09E2E99A4E61C4FA914D
255A3E79C7A757253839A72AE38C573DA463454C220A798BD972A26C115EB0D8
DDA1A624B846FAC41F13D669DB0B46EACDFE40CFFF07FE1DE117A1AE42CE00B9
E4281E4581F48501B9FC1D6EE30A5C162F5F5D78182CAD9AC8546A64E0285B29
EC86ED96DFA8106C986FE495D11E54B11CAA7DF823B10C5E95F4239381DBE451
79F8DA0E79F2168ADE07E65F299E7FB957CF2CCAF53250603D68D6C2E452F42F
3BDC60A080F8DE9D4C6EA16CAEDF50C250912725621BCC241947B34185362891
32D2BF71CE723B0A3E3673E030C47BE983C9E12448E22A3DE172F1EA35C4BA01
587D1BAAE54194A71B7A7606B0407A2EA48B20BB1DB9D13AA061D88691914F8D
A45220AE999CA189F5379421655748F468FEF37A685C78A795DF2DA3B0CF6971
CC2E92128853ACD86F7D2E65286999110B4434DB2576A034C671F24801BAF06E
49D0315860E64D02BC9297708698E1317AFB7E86D2086BF544C748D149A58811
B4518793C4E1F21F03F120D7778A9209714CEAD4E54798D0DA7170C88B7F904E
40589721B775CB6847F637F76DF82D0D8E36EE5E7EEA2EE6624E158763466A9F
A7314D8D4C979949E089E115C9A8CFE5FF7096F5AAE74D610F400C948E8469F5
06484F21BB8BF37EA7A3BF5D2BB12CFF86BBF4E10344365C3AF92946694A0F46
67177B07ECFADDE2AAAB73D33C0EADC84B389270B375B05B7E08B6F57FC5E83A
3EE961ACDEC1D5018EABE7D86843AF998EDD102C7FAC6ABF165FA3A29323BF2D
A6928C33AEE0DF1F965E052680D86F4DD7A1A76A6677207F3CD92A25F8D37A2A
FF48F1D9D40652DF211544730EFBE82764E3847E3490778A15C42B7B37BC991F
E3F3A8EA6E34461AE4BB63D3C34A530B779903A42E51D0E4CC3BBA88B5E6A8B8
BA7C16FF0043E26F69341C2C416AC64A97705CC05DFE89316AA647AFEBBCD378
5558D8407C370C6130A80693000FA771CC44107E18CBBBFBB71A93FA2E0B9562
4BEF1D5A47A1D15B00282B57ABC3350A6A7136A10F2DFA2996D58C61B7B02C8F
225D25F93FB1EC6F473188B927E7572BE4D3F826853E597533DBF69738A4D1C0
086376154DAD79C2052DEAA5BABFDFCE62A9E74117FFD1CC1F41021A00EBD754
3201C15F4A4D1F9A5BC11F4C07323411C4559F87CAD019DC62F3028661689175
11BB2A5E3A98B43787A08EB022C4A0D6F583CC054B688D77433E1EE9501481F5
B4C92EE34868FE1A82C026CBB172DCFC82FD09BA17BAF41950A08B03991059EC
1989DF3D307708C4B2393E68515CC8A6BB2B4721EC53E42C46842B934E4AE1E2
6E8E95CDEAE95E8802DB42A288575293B9EBF1516D90ACCF65FEECC2CEB90CD2
E1658DFE5287976F1E810DC62EA2E7AA8F3B96BF6C723510417ED57EB9842561
832A5C6073B617A25491D79C358D4284943E0B25661532B7D05BEAA0B5E32FD2
3CD549AEAEDBADB8FEE5B8E688E4A31A39EE4723ED15EC5AC8287FCB2E8AF2A2
0EAC6083BE3F66A8912E05A7D57F94396BF682435A42C61BB8B8CA7F28702AE2
E1A3E540AA9DDDCE01B519745B1355987628AC68F75102F1C36EB1531FA904F3
8FC210DCA9907D09FA089DEA7728B92860D933A00C28434E6118918624C41CFC
1B8D63CCCC594DF04FAF9E3DE98E44D71D364FC891CC923DAE5DCA00997B89F0
DDE428A2E98313581D8B450C4E7017F7231EB6EF661799A0EEAB60F68BDC189D
70F76506E20409162DA77D077F1477889E4C96E1BD85314C8D5BC2304780C1B1
BF499D8ED2BC3F4CC3718F9DF76AF4681F8AB7A378EA1BB56AB08A9AECDF3063
4720229A8F61856D93991F0C12C6BA63E191C1DA6BF3D63B38B0F6DFBD53C780
3CB411ADBBA3BEE9C8C2A5547B67CCDAF9A958CF9BBF68D0AB4D0E20C8ACDE98
D0AC9DEC6B98CAA82ED89A9D9417C66E3F5678FDA269F3FA07837BD334D29DE3
7C402622CD181F98B590A284DF990159164BC7DBAF1ADEBC3AFA80672B1E4CAA
15FC3354EBA4B6FC8218886131D46D999282F749CFCD00F5DDAA03C272BF29F0
3DA2833DD6B20852B7EC36DEE891277580DEBB3A4AF33890238B3E3B4B3FA7D0
8AFF8C27D451CA7281E007C06DDD4AF2C4E266CD545337E25D685CEE605332C7
1650A42EA9FCB9C4F70D93AB76E692FA6B06FBD7E684A9BBD4353BD1C527C747
A95BF3B9FAEEC82FDCA86B876D6E378E26C3FB32399AF231D619F05BC6308728
3409A1B503A89B768C1F3B7418762A024CA7E270AAC6EBB9D98B00894958867D
8EF86548874BB071968C6CD23E8C312387302A76127F40CF1C0242A44B40C832
212F835D78DE0E1B33EA7540508CD7E3E9BF03AFF2F7F6BE6EED4039F8515C33
5FB911059C01F6F242091821DAACFA51942A829A79C3C4F80556F829A3608A5E
9063335986BFA733595AA6927C97E8F09424F2CB9AA1AF12A3452AA23C5AAB99
A95DD057BDBC39F9E3FE702A21A77C7B4A25AE619A55973074B613B0DCDD2B2C
EBE6B3B9FFAF9D55606ECF8FACF4A138D2D1D2448BEA067BE578F656A2A2B120
9890F86E9E0A48B80A9E20DB1841C4047D01A34E68C30B221BEF99DF91A42484
407DCB62CD3940382AA7FE883CA4BA5D4084D758F41B5453B5CF59466737646E
A724361C9ACF555350D6C20DE7DB3AC301891264BC06D364796A9339AA05E553
DDEF11E418A75DD95A15FF088EA3A8FC1199323A46C5DDB7035C0BC0829D1CF7
6E75CC576C934DDC54B578F6C0CE2326932632F968B2A899325D353CC1F3CA21
9BA71629DAE872E6A22F4409CC1B538BE549BE847561407E843394A9042E61D0
95C6752D440D68BB212C31249CCC8AE4BA11FC4F71E704C8B61F6ADADE070DEF
082A9281FB592BB70805C365E191FE9CE3F404C309B426E270B3C642A91EA483
3CC4AD1F9CBEFFCCBD2AD05D98D0CCF88627FAB819F45B49E98B18BAC003159B
7A37634CB67AEC4F1A4986B0299DDF0CDC623D17A88DF07DB64B9DFD4B6CF227
E822A80B04B2AAD644E063F5D276A3CDCE210572798F86AFBBECC97CCA25A188
844D68AC894E50FAC14CCC9612FF4A42FAC7EE8A3D1C03274E68B010D71C1C5C
CB16EFE665CD7592F854AC46707DD0C88081FA7595076444D8410AA7FA181700
8566C80D5CF41C3829D53EB1C9CD669F6CC96A02F945DC3E555DE134337AF8B4
FD66F87CBFD4EF33CF281001E44452AF1135750307FECD3FF6876C6CC6D43312
09533E9A268044E95506FFCB9DC9F4042A33A6E5D387608BF2CE4650BD16ED09
C9E9678E9F7383BEB7E4F35A2D247E13182B720F26B329255F22FF4942015865
6808CE3A419405358B449D9081B5972E800FA8EC72DDEA45207FB4F924C7614D
68C971E06A868A14CF4524246062FF17F48C7825C7E640EFD287F43BD05EF86C
24466EA91D043CC9AB87D32489DDF0B6B803725AE0F38D3DC33D6109A8DA141C
25F95ACF80F91AD04D342CA23A6BE3C33C86510E5BCA1E816A0DE071ACDEC301
9FA42986F4B3FD547474C20F6EAAAA36749D6BC87E6E4C36AB34C73F322764F4
B779DEF9DD0A01C48666C6759F951EA5DBCEFFA43C4889310D6C499C423A3701
9AC2F45B5B820422E618B76F369CC0013304F97285D95997578ADDC5BBFED5DF
1316149EC49C3BDFE186CF1CF3C1AF9A9525FD2C8E5A7ABF2547B2658535C61E
F3A656F8A079AAF034090F7F47361BF7563A1F808BC2EE82F59B56D5C5352C76
AADC24BE0EA1D3FEA3B98BC8F2E25943923FDFA8AA6945AB67EED37FC7B5F62B
27B53DB982B0F261DAA888ADCF76776E89ECEA3ABEB13EA1954FAB027A348165
04CD3322E076F10A1B665EBF9606602EE8F3E7152692027FEDA80CD8D082362A
BBE70DD28DBB7941D2D9A839DD585601A92B96D492F6460999194FBFFE96635D
5476873797746A91AC3A554E8A788079DD5A9DE06B7CD0FD60D3DC25F8BD859E
79E51E4DB235BF6CAD95AF8FB2AE3803F85EA543F2EE03CCDA38CCA7962AFE8D
EFC442964E8DA1CA63AA63ED9F3B4FF8393B0E436223BEC535EEDF7239DB201F
C4AB5C2BFCC21E1CEFC65F9609C51764C5CBFEE23D008B5153323114D7F1FA85
A5BFA0B20370BD7CDED05F196B265BAE494E2E051A5027A070639CA6743A0F9A
6459D9524C9F8B4FDDABCBAF5D9F674EFD9D57C1D524CF69F3A44E42A3EA8022
6C7F7851E61D0780890BB0C1A492120D2E8AF921D21044AF197307D890632505
B8509F7F734F360431A1C5A77B622D8AF1E6E1E94A120D7F91FE06D59E215080
86EF38F5D04A9B19FC7510F3C6E3E5B2CCB7D8C729280FEE70E9D0704C780852
64BE8FE761AA74B47D8CE1D6FCD113A874B3F3B2125087B95A3863502BB86CF9
2980C9A334C9E6C459A02D8E199DFE6FDBF4EF741AB1F4B888780248A44E4348
B71048EF9269849AE3552AA3FD04FA8FA95BAC0D4144F1264A42BBB36EDCDB68
3632A625BFB2ACBC1FA9CE6D3DB368C7B19E35B98F34F5B2690497D8D1867312
C2EF852201ED7952079402208239CA8E4917AEE80F4CB1090E4E56CB46A97FC2
A404D8FE6440DBB5EE0DD15FC708D69123432ADF76E4159946E4B0EBB121E3E8
2B23763B76BDE8EF2EF3BE1BD5351937FA1F83299512FE1BD586A0026B2B26C9
E4457E7EC551EC51221AAA9F28E0D25C6A98F4EF9439BE0DD071D5E3CBEA2338
B1485A189BCE8D7AF886EBA979837F6B8E59967C5709790BC9B2E03964F9D59A
E93C36D31B49A2203406DEBCF1C06FB02DEF76FCEE09B4691139064F65FE5F96
FF76780179A6A97583F2A1CB60BC0FAC24B9DECC8F19F57261BAFE22329D31F5
47E6B7E12461460DF471C17E3C444C03463C0CA6E449F61D2F6AA2F1E298567D
A40B75668316FEF615559B60177A504AE39E9E7F20EC4B47DDFBBE62B176C6E8
00E264D50AD41761DC10FFAFA9BCBC581BA9C73ACD3578F3AD9CE6CCC9CA67CA
2161C1347662B3B3F4987D3828F60C47359F1871A1470CFAD4EA8F1945933CF4
400F0A0286FC00041F5D639E597C851BDC8C64B427ED7E8B344FEA4A42B94DC5
E894CC543F53D9DCA18FEBE1691F3B25AE84F60E4CCC8FBE81B8F65A90E900BD
F963DA868381504BCE7BC8D2EDEDCE91AF11A3E1DF384F35BFA6798B71B671EF
7A7C75CC7CAF5E6219858DA332C1010F8F2C54EED24DDC47C0FE860FE534058D
24768DC45867341A90CF6F5AA69F82C246408B47E5255B34F2164F0C58BC0F7C
C57B2024CCCC428D9CEE18035C99B6043D6D3AE742BC8BC48FC6A82DA8DEE745
EFA45639758CC0583427A9912327172A52F3B0CEE25BF4C08DA19AFB5BCA8D66
C7A581031D2C8140F44D608B7162801FB2DC7474458FC0325A48914147AE4A5D
F655DF8D210CA31EA03A9AE5E8C4612CF0FF19703432D66A168C372C91596C24
7E8438C314291C1160D68434FE8AE382A327D17531715D57AC4A67F077B8A948
CA97C52FC4AD23782B923D663FCAC9EABF7312544530F0F0BD6A06BBD1B48CC9
45E5D34F77C537EE33063B448045BE80199A3BC99486F444127A43B9E3DBA7EE
62850FF9445ABA094762EAD6FDD4AA5B5FDC3B59BAA4EB72C417125DAED57F92
9732BC2F277AAB6AB7B10E325CB3F48CD4D00D35CFC66D75E3D5ED92CF3C3771
AE9FA775B0E4A191D609E5282FBC15EBA9F830E350E937A1CA44BDA79890F1F1
9075FCBFB8ED0E315B7075FF75A32035408D6BFBCC270A41F1341EEAABF9D293
C9075CA4B1DDFF1D07C72FBF815BEB97B533DDB34406C296CB3CE25F82721452
A44DC6BCD5750AF5F0C2E259EF396DB97917BC9B22D05D2C2693C22CE3086DA8
95171E962FC214785655A93809C9936D5CE26740C3C0355484560CBCED757483
3184BB0A7EF61BD69D1B23F01E624C437D266B83691D1BF6819596E490266E1D
9FA22CE8CC5BB48DC5111D44B6FFFF05DCAF66488C11CF15EEABFF6ED677C860
CC5A3E160FAE3CF936904EB673A66041E2C7AC5830A1BDD2A424E0E6EEA3B64D
62160855CDC53C5B97DF6FB63B227E6E710CA393EC0B6BA3D5620C5F861ADFD4
FEABFBDC68B47B91EC13DDC98D771055B3BCB703E6ACE974975F284C332387CA
DE4A3E83AC63F64CF2C11315D8C4D3BC34FE52936E8535119F8A8B91E9E11A55
382E3908AA4A81D01B4B1E53C151FADA57B9F9BE33718ECAFF9396BAE1E30D08
91661C4A152C29AEA3B95822A41B82DC3B8F07BA006CEE92345B73C4B97C49AD
1C470AEB71D0B6C714B7D2238CDA7F7DAD98DEAC8AFDCB98A7494BDD401D66A8
BFDD1E55E7A57B96A1F94BEC8A129AD775776AF3D91141247CCECFEF5DB10312
D71EDFFDB5C5985BA61566245F663443F63D2FD444291F376452CB05BF58D165
87ECB88F6BDC571FB15A49C4BF2FCA29A26CE7C33A8EB99A49319F69B7AD611C
09DF8F74EFC6227F7FFC5C35A462660D52B150F0CE2EAC76B6971BE6523C19D7
B470EDBA7E685642E71E1F312A127F53E016639E04EACE95F154C1F2DE4A75AB
AF42FB5D29193D79F14652C47F279B4370497EA40052C18FF2FFE0136FFC133A
3931CC576DC7E7AC4A2DFBB3EA1CB3FB854405DB2E7732C7BD7BC4E0D951B1DC
42AA1EA635CF6E2EE31D55AC0B75F65BF834F222C10D77F08251B1001707B37A
8345432B03830B7635B2111ECC447D15883DF062835C24096C35982404D06A16
367F665E753D4453A90C6F73C27CBB42EEAC03862CBC830D9F8AF48F211CCCEB
81DCB3AAC6CEEEE8583F7F93C81CD09F1D5DDDDFF534D3143F094F16878AFE42
C9005E52BFA159163DB99474725A94D0C248BCD4299A97C6B00598CDDC51C3E2
104FB63F0945783CFFF784D20C9715D671095292591ED67E7B428C758786D458
E04350DE22661A88FC1DF4DD0B54F8205D1203442A501DC16F090863996FCA78
A42A094C3390D9BFBEFFF8994E73158087C07BF9D92C561EC5B17BAFD22E7BAB
BEDBCB5393A2523494E36D1823542D44CC7FE667CA6BEE5060CE81204A27A71F
D200E1546F04D356E633429425FD97906927EF198F76DD26FB86BF3145AD22EF
F0CFE876F155883C5285C9ED015122E1DDE383F18B487138DEE278AEC4298835
3CDAFB2C765F727398D3573207AF0B202F3ED2673AF165BBE3EB5DFBEE2EB85E
E5AD5EF755D002FF4DB3731E0481379314E25F39CB45C50F2331AC9340BBB551
8E8BFDCB2CA774C358CE6797125BDCB2A1A793C6C2ACB564B69588D2A3A48953
731CD772BFB8100973FB465CB141924238189FB5EEA5B28DEC08E217FB57B4A5
F0EE1FC7F68D756FEB84EDFB7D1AC65A3855BDB4BC209E38A3590C5C6417BC40
AD18A717AC45109C60AB19479E20CB74DB2CB1EE771410E585F393ED87CE0C3B
3BCF8BEC554406AF6261173BFED87467A5967DFB4E9EA7859BC81873CFCB31C9
C5EA7AA198FD3B7BE1D720F76CBDB04248F369274F6121F92345CF910CCAD401
1022234813F406DBD0CA005E793450A09879F1915EC69AEC53D1A70FFF0A6A41
C9BC518E31B3D172513AE19654320665A7CEB5925CC25756C119CD14B5D31911
0725C03B2275B047E67E08D02AA47DBF6B1C04DD919A9D8AB1D5F52481891226
339BFEF2094170889E48973048D2DF1B00E7EAC156EB92A7ACEA043C2E411D35
99C8D27E32324A1DEC9F553B077B5E185440721D1BDDAFE42DE3BBCB1AFF7972
EDB6375B7B6CAE63AF0E61A3CBA69B720BAB8C52C2AE259F38D004A1D985DB7E
F018299B0ABB6A7FFDAF70F015470F8DDD64D9B456D9E22F69FC6779D36EDB84
35DD7C9F60C893C33D2D15A1CAB5B216F0B2BB3254AC0CBFECF26A87C5BBEDDC
6707BC9DC141D5581867664B6C19667A422A1C8D165188E57DC8BA313C6CF586
AD2CBE63A38F0B0E285A8F4313C451923A882A7F94637F51D755DB5395322487
55305F6AD2A5A3CB0CA6DCB840B496F88FF830309659D39DBC5D408ECF946735
508AA1D443F4A586699F9B940787D25E52BEC550D6C02AD6CF478A511F2E7118
AAAD7C5A162ABCE09DD5BF49A06AEA20A9117723895E07079F899CBBF9783AE6
1ECF2642EB695042753E3026695492E9543BB147FC93A46ADFDEA89EC079AB62
19E059C8FC2C822A5A760DB73372BE2976D5B2539C1EA36B5509BBAC435B6206
EE7EFA628FEE45B0D70960AD51C41DC6F40B0CC381FE7261BAFBD79DB887525A
455A2AE7E3D9035E8C4B851FA40EE5C9CE3B9A3FD826B40FD4DC5EE26D388AE2
7BF3D932AA34716492C0DB7FC0A7F427323018C3D6F6DAB59BEDC0055697C429
6D6117AC3157FFCB20CC8B97D01A8C680F84FDFEB2F8C6721CCB6FD6D307F7D7
EA3CE05F6F153EB672382580B225A925512A5E97FF85F4FC46BA24F80EC6AEB2
26B279A306F4D707375B9047C11C7E7303C8ACE0E2782644977D91BD0416FF1D
EE6D568C93B7CEB3EE5896CE5C2E196870694C0FBBD9F428F2BB1156505D0878
9303968A8A354FCA750C016D92E4B94F62B1987885CC79E04168D021C5E642DA
9908AFD0FE906631A3410DE62A0388BE1B4576FBE88C151B2CC446BCC0441044
080F8E68C7087F2F7EECEAFBA168A22D5A5453870DA96F2BAA2FBF2332661528
3C6C6C3BB9D3DAC5F0C83C45F1B86EC99F389919FFCD3CFF2A837E21F209F7AE
26730D7E9DA01536F5E5560378F9E86B270CAD02A6B6AB6D5303566E2F6FEBCC
1DAE85DB41E31C94C591D912EFA9CF4AD1E31C311C4AEA0E70C60E26D7B20B97
15FD80C02DE35EBECA3ECC23694A3795BBD432E9C40C0BC30065E75DFAB2A865
1B1B4487A2D77DBF950431AE441F9FED99E680582EA1972D7966E1F21D15070C
B78557F16501E9923FC6C20B0D24CAE0858C5583F2F64C1DC1889789B225878C
7B4A3566937B56FBCACBE677F97ADD488887CF11214A867F916D18C23D9CF72D
00CEAA007FB51EA6CF84C7DA36AFE5733BCBD3C9DCC5775800C72CAC88FC6E3A
481D173EDB4A787A257511E0C0443C6002EA66CA8651AD1B374CFFD435957DA9
3593818939E9132D471A83427FB27F63E8825CFFC14C17FEEC6CB70F79957B34
EC56C5FA8F4FF8EF5A00C668034CE9E70604368649AC044642E8859E87237054
57BACE7A48AF0CF4B933D0142FB604B5AC7482BECDCA909E32977C98EA2777E7
AD0A91BD36D224968FE2784E45543458031DF395314DFF7E173CF486743806AF
869E3E1AB6B3029D8689E9AF4C60BA2CEA95892A0ECBBBADDAD1A6CC248BAB5A
8CF64B537BCE3DA0616D8809238CC4F15CB0691DDE6C3EB6BF51DB1EDCD3034E
A1283ED4BEB49469CFAAC2074BF9826CE14E23231C8F4DB1FA5C13A8A4D696E3
E1AD6CB31E7AF12BC92DE8C8EC6C502DA6667783F27460FAD9AA87B1080B4EA9
899369CB7B7C53695C7B7D46D286846BA1B1C675A98BFC8E15BAA717C2042580
9029A0A13157BA15AD62D6708CF8F2208B153999C03A53C438EA052D184ABC95
6AB774B323A0AD4D9F2923D65D292C7599B77DB6F001CD0AEEA9C0DD833AFFCF
C537CC0825FF37A2ADE329CCA2F6856F18DA201C70849A7F6153410803C8F51B
CA0A113E145E4AD684BE51AF19A96EC039CD6F81CF484A2B8517C5B7C0276C64
0EE7A2DECE2746439EFE13E547A0A1FB6D3CA975835E2CA347FCE8254D5AC204
4E503B6DE4B531FD7FFBD959E00AE31C6C9217065366DDCEA0B84F6602A075C2
2F1D4E979459B86BCF9C00BE7A96FCB68B0E89E8ED45E1A40D2D4A4114ACE2A2
FBB48D426803A3959243EE83C569D28F6244E9474566A836DDB4C289C807B6F2
3E3C72DEFE30458B6A5203949848185F8EB82D0595A4C09A6AA8A4141C362726
907453040EEFBAAD77AEC9962D8BB0F07E863D5363DEC5D14715F796B8E12B88
273BF0B74EE5EB7C8D7046D809111EEF4F288A8580E4B13BFB03B3572117F188
B732673B597B79B7A85F6FB6418231109AB248B335CB61F1F9F387C891CAA7C5
24F59CBF222D931BE07B8FC4E7D38117DFC38145C2ED2A9CE09E5DCEA857CEB3
358E4D7E08F4C633832A811F22E44F4CF5BF926F0E4B2A24B902028353FB4819
4B187CC1E6861646F4D347A0DB9E3CB2B9A34D3625F3D8926D469C3E625E4526
92CD543829E3D8A041FADEFD201B9815DFE7212B2D0D7ECF7D3F901B5D2EC974
63D5B53D751A4A365CB9244ACC2D211A2288EA94E95B50A9FD7342A0EE1E8EC4
71E0618042A4D2C060E79FFF4F62A7517536C67F093C26A89109E7C2CC98A4B2
C8DD1AAD3AB1424035FC7C15B4F37E06713FFAC97B88BAC7A2CD9F8B2E30C662
26D555F87CDEF7F73D45B117C3FCAFB4BEF6421AD410FA6B795C2C0576FC653D
47AB5459875A909F23C5FE7184660B8007B5002C2A8CDC5B703B28CFC11F3162
295E7CAA9A23615E361D9970E073D671D5D018A06D5EB2E372B41DB3181BF25B
632DF707A82AC5CE587B0C87BCCACE53AB5E8019A30F868E4632BA577AC7FE2E
5BFABB28E7FD4FCCFCED74224C4E7EE09F483F1E7092398FB83A7514BA8960E1
BB8D020A08EA6B77753A1900D381F15EF1EEAC0BC65CEA72737ED849A1C6B75F
5417006AEA7A5877D3E17830288C014809330F495F6867BC9398938A84ADE86E
8E62F36E59420A52FC9A5F1CA9E50C7060ABF73EC009A13C84B2FA06D777C66E
1B14C178A006F486F465C5C300245BE60565553276E305F1A714CDFE897D2E19
4EAA64843367B1CC6FFD5F6EF8BEA7985BFE011481D0FA47A5362B69D8DA30F0
E2B287E489D4BD83E3F82F60F53417943646BC502BC652028A5681E8A815953E
A283E887ED9A96C1AE013DC3D425FF55552260D6113C2D97E110FDF3A687ED47
4F7979BC907F045244B2E299BB473E97B67F1A9D38DC8D8E251969A42558B506
B2E88A72530E527F4BC06E460997DE5D6AE297DB3EAF0E7697060A53FB18542F
90A4EFC1A1808C667861699719CE7D56E79080FD8159DDA3BC8070DCB73B4D49
B43D99D649554512A04E0A0CD28D2D5AE80DEED2C9BB3C7B3F56AD147EFBBD01
229AE670403222E0B741B9347704B1675A5094E7DCAB879CC2DE626B9C36719C
95F5A1ED6A3013529EA5E81BE0494ACE0799107DE7D74C36024BAF3C5DE339CA
F2A854808CE35EC091E9C48360C3CBE510C75724409D719F508CAC33327502E1
767146FDDC7B95BE9BFF07997A3E64D36A94AAAA4B3F96DC27DF4D8590DDC2D5
3ACC9AC3781BA62F04A23DF6D215FDA0EBE6BDDDF7777E66354050F988B4DB16
53EB79BBCA4AB398B24E5E7771A08B482DEF95BA49EF704079A8E1AFF750B3FE
5436FD139A289E08DCBB7B0013B5E327F2E502C369EA434F56937B85714AE180
46A72ABF81D6CC660CA24C01A699FFD8FBD2E9A90B006DC07BAC8955A99E7A89
8B81511EDB96E1208B03FD14797530B074D142D7A06A0291405B99D1E18E2486
2FE8D3807E2E5559A375F6E8774EAD3230A3F49EDDCF6DFD71C3702DC5C8E6DD
FB49007E68B3BE2B0135D10E44C4BB4EB1D29F2E5C4A6A3656CEF574C2523DFA
2648FF7B1D7595C28F93F1B485B8129FF88C1FE67FE59BD5E7369C37F2920E7D
70D93571B035C670052DCCBDF6E64E09B40AC22E20CB00E57EF40A7ABDAACF86
A06E7FF26DFD3C80B9ED864F8D0D9FD0B3F4AEC63AA31F263D43DBBA06C33E70
DD915A8386778E041B9D3A936134155A397DBE5182CABCF0F823116606A03D83
5CBE06A34F65095E12957ED88798751BB14C09F114BDB7F651E10370A292567C
7A75268A0EF34FC86FBC618D34FF3CCEEB228A77FAEB92161131C783047FC416
84A6202C714C75B2F5628860BD5D1B1E0E065563390BDCA825FE76BAD3FC140A
E22B229598A6DC2751720CF49114E516E06163E71A29423CB453A5E2C6B153BA
67A393ADE3D042570F964C21F0299460A8490C0A4AA654AFDDD13C3E4503CF6A
84213185CD963AA1018471221A7D3B38A9723089A2F6CB434C2DFFBF15BECEEA
1C79CDA92484FDC756F9D5181B08E73A800DA5DF12DCAFCD2425888387E63B64
D41D42BEBA90B36C93EDBD13A22C1080B9FA39EC84041F9DD57FD14F5DAECFBA
70899B76A9B616614F715642E1730962371408903FF262A4F63DD006AD288365
B1AC0E023B88155021CFD3D8C6009780265C0275B9F973441109B2BC1A52769D
FC518DB70D664F5B3ECACA0810605B4CF0A79F12C84B9A45458627F091EAA379
616656EDE7E9074327CA5FB42FE57A30072662ADC52131FBCB0586FE6865AB1A
AE63D931444926A7347A69452C204A47BAE23E98CE7985AC4697BD9F46AD27BD
7222F95B15E19475DB684E5161A64958F20CDB4BA1CEF7F49B99D76F8518D4A2
CC081654B16FA2853D2B4658CE701F1EED09995E7FE13944E54E8D9980ACF12F
DED26430459D5422A17D1035641997C897DDABF83634C64216B94379B78248E0
0B35C21A6A4182B1A209CDB91BA7011640CD46AEF85CBDBF6DB9672201461C84
690FD741C2D54F93008BF551E8ABF2DE346FD8BDC5A7E2C69228EFCE149AD5B6
D4C941B02D295577EF6A18B7224358171E9A71916C5A9E28071FA65BEFFFEF0E
1793704D9BF9B42A10F0CF6118024A759BA87A0A214752EEE75C93961089DC53
E2AEF58528558EE53C68C8691F7E164E5DF015B80B6F9AA92495FB57568E806D
D6A212414947537AE1DCF48ECFF73E3CBBC9B77EB2503DB3091463CFD5D88E84
0F9B97BA05C5B3C98746C014885E42E00381C9CD33E1241CAF226570E46D5A01
127AC4C28F1F2BFD3B184EB75CC8E4313D5834455A9C5C58B24BD9B44701859F
3E762F22606545E1B6822EB1FCEA21FBA92ACFA489508DD45D9152C11F2E549D
E9D774BCD5082ED2E1AF6705C01B4CCD025B8D408E0DFA1A50C88304FFC4BF57
7AB9D9416067815E2B77E6E775BA56CA202F6D025E06DC7F8F9BC4D8C62D0CE7
CC82BB2EE876EC0E865B785CF513199EBB944F33CF528FFDA2482218BC8E6BFF
A5A01A88E30C3B088B207385F1259E4512E030B2634BD63070042EBF6B914620
B7F74D24FDF8F304E024A26CE18F044FAE4928388149A5AB2C31578AF5B853D4
ED4B0A38CFCAE442A9558F064CC7968427E14F8B4986A7C4E7F38262E5108B3E
1234AD0A051371B817A1FD7F6B1A8F9B438AEDAD8512B6B98187C62648BE3B62
A1D375A937CD3A9AAEAB4F5D97149D12BCCDEA58FD4F5072F7FD6882BD73A3E5
4E60EC3AB9FB6C937214A5223BB2A569AB372B04F9B92EC67ECBF98D7EAAF670
133A0AB1CB6C6FDB4B61BD7D6F4563F20E64323BC4B8AE89EA1A48E198EC0AE5
64FAE8FA7080AB0A03C34079069D5021A52697E41DC6
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMBX12
%!PS-AdobeFont-1.1: CMBX12 1.0
%%CreationDate: 1991 Aug 20 16:34:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-53 -251 1139 750}readonly def
/UniqueID 5000769 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: MSBM7
%!PS-AdobeFont-1.1: MSBM7 2.1
%%CreationDate: 1992 Oct 17 08:30:50
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM7) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 84 /T put
dup 90 /Z put
readonly def
/FontBBox{0 -504 2615 1004}readonly def
/UniqueID 5032014 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMI6
%!PS-AdobeFont-1.1: CMMI6 1.100
%%CreationDate: 1996 Jul 23 07:53:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{11 -250 1241 750}readonly def
/UniqueID 5087381 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMEX10
%!PS-AdobeFont-1.1: CMEX10 1.00
%%CreationDate: 1992 Jul 23 21:22:48
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMEX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /parenleftbig put
dup 1 /parenrightbig put
dup 12 /vextendsingle put
dup 16 /parenleftBig put
dup 17 /parenrightBig put
dup 18 /parenleftbigg put
dup 19 /parenrightbigg put
dup 20 /bracketleftbigg put
dup 21 /bracketrightbigg put
dup 26 /braceleftbigg put
dup 27 /bracerightbigg put
dup 32 /parenleftBigg put
dup 33 /parenrightBigg put
dup 34 /bracketleftBigg put
dup 35 /bracketrightBigg put
dup 40 /braceleftBigg put
dup 41 /bracerightBigg put
dup 48 /parenlefttp put
dup 49 /parenrighttp put
dup 56 /bracelefttp put
dup 58 /braceleftbt put
dup 60 /braceleftmid put
dup 62 /braceex put
dup 64 /parenleftbt put
dup 65 /parenrightbt put
dup 88 /summationdisplay put
dup 90 /integraldisplay put
dup 98 /hatwide put
dup 99 /hatwider put
dup 101 /tildewide put
dup 102 /tildewider put
dup 110 /braceleftBig put
dup 111 /bracerightBig put
dup 112 /radicalbig put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueID 5000774 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891
016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171
9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F
D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758
469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8
2BDBF16FBC7512FAA308A093FE5CF5B8CAC6A7BEB5D02276E511FFAF2AE11910
DE076F24311D94D07CACC323F360887F1EA11BDDA7927FF3325986FDB0ABDFC8
8E4B40E7988921D551EC0867EBCA44C05657F0DC913E7B3004A5F3E1337B6987
FEBC45F989C8DC6DC0AD577E903F05D0D54208A0AE7F28C734F130C133B48422
BED48639A2B74E4C08F2E710E24A99F347E0F4394CE64EACB549576E89044E52
EABE595BC964156D9D8C2BAB0F49664E951D7C1A3D1789C47F03C7051A63D5E8
DF04FAAC47351E82CAE0794AA9692C6452688A74A7A6A7AD09B8A9783C235EC1
EA2156261B8FB331827145DE315B6EC1B3D8B67B3323F761EAF4C223BB214C4C
6B062D1B281F5041D068319F4911058376D8EFBA59884BA3318C5BC95684F281
E0591BC0D1B2A4592A137FF301610019B8AC46AE6E48BC091E888E4487688350
E9AD5074EE4848271CE4ACC38D8CBC8F3DB32813DDD5B341AF9A6601281ABA38
4A978B98483A63FCC458D0E3BCE6FD830E7E09B0DB987A6B63B74638FC9F21A5
8C68479E1A85225670D79CDDE5AC0B77F5A994CA700B5F0FF1F97FC63EFDE023
8135F04A9D20C31998B12AE06676C362141AAAA395CDEF0A49E0141D335965F2
FB4198499799CECCC8AA5D255264784CD30A3E8295888EFBC2060ADDD7BAC45A
EEEECDFF7A47A88E69D84C9E572616C1AC69A34B5F0D0DE8EE4EDF9F4ADE0387
680924D8D5B73EF04EAD7F45977CA8AD73D4DD45DE1966A3B8251C0386164C35
5880DD2609C80E96D1AB861C9259748E98F6711D4E241A269ED51FF328344664
3AF9F18DCE671611DB2F5D3EA77EE734D2BED623F973E6840B8DAD1E2C3C2666
DD4DD1C1C9D3E258A50C97878EAE284166B202FBACE65ED0F2F801C3E2542C4A
9315CC1EA9684A23DFB4B49176A4470D8F26E85320CCB4818AD7674809874891
C8C401FB4C09F63763EF221CDAFE83B577E942CAB60A0F1FAD753C7F1AF25F73
9CE5793206CDF51A2B390743BD8CF8BF7D0328816C9270C5F194DD9D565FB612
5FA41BA00E0F57F1705A6E11AC460AFE3A040B2E2C66A92F9B334F313E3154EE
CD80EA307087D5E0FA5FE2847A9BE1EE28EEC88CBBFC8CA6AEAA170B9EFAC882
BE9827F8FF5C1BAFFC142F1F73668AE1E177EE95590FD982650B3876D55DB246
6322A621E2BBC387A162AAAD3E9FD783699E69282DF9BCD1CB3CDBCE9D12143E
6DE2E1905A9BD31A1D10994D91B4DCAB4C7ED065A0AE7DB05B9874D370C883D2
90CC84C05A8A83A2E4C603D59ECCE04D1C2616A0E8552FB211526AEA0C6C52E6
1801B2990DCDB412BECA0A908C020704C8662779BFF502C4389DB2D9C25C65DF
E8418FE866CC3D69B3FF6790FA1D8092A6AE9E222C4A48624C79476075CB322D
1F37BB54806AF0E72A6F9B62510AFB7AF26E08A99BCB284F07F21FD6D273EB6C
70B9794F7DA427D50464473C78FD5247C6EC0ABB6E973E9D86B17D6ED175C8D5
9CBE62B837A1DE54536053BBDE962121A92F4EAD42434198D795D95959B8B6E4
C5ADB46B2BE981E9545D2CC5B9AE95FD7552AF0536EDB3328D9AB16510FFC463
E7484A477C755BC97B0BF323BEE65D99CCD67E3657DD29BF63C2E729CD561D9F
AD9733E5814DB2CFC8828DA3C8F19384D94512AF12BD87587F2CD29814F96258
12A933C13699B4A00A10557C24713D33FC4EDEDF1ECB24AAC70F7DD77B4D68AF
C20300378D254A9121BC6351771682249A4028BABAD6FEAB2B0942DBD5ECA64D
26B4201B1C42C9EE8A9A9E664FE08556A90E828F692BE73EB78C05A306B04C4C
75B3FCE338A1FAAD0FF0F2DC5E9840848BE643A306BAB56CE8449EBC058507CA
9539BCF51AFEC900ECECF694311801E321E3A9EE3B158FC6C74A8FFE0F8F8610
B54F360E13E5E9C31356FA71AA674D88E08B7357D471E8A28931CD16898CA3F2
191A73298165EEADC5799173269A7A478EC984A7F4E59BD05EEC8A8237C70718
AB10DBD4A155466A86209D1EB13E323C836FD11F8057FC2BC78106D5441DF7CA
398C1ED76D83BD44050DFFB0A20F0D17C65A44AED1951033D766EB003B4DD16A
486CE90B8AE91AD4DC566E34779A5B75F551DD087D055C2E2C25281A54750377
AD7B0A580F9A34B19D5F6FBDAC53E1E70E8F266AFD8553593AC21D7C7C3A5009
9F46C77175AE2D39F6839A9DBED5F7DF7C5FE820231A28F7DC2134223267543A
6CF60F3262A9D5ED85E1ADB1F51DD3314173CFB6162664A0D0183F7298B2E3B8
F2CC0B89D5FB3ED6BCA5BC3643D4065D9B5B776925F1B34A5435404B84861459
5065F91B8002AB424C33DD3309F630DEF55C95009C7E8D910986BAEC3FA2D22B
7180D62F6FEF1F97CEE474C12E3C05F4353617587D7CC55B062CEAC4CF3115E7
5FAFED632ABE7EA2E80C191AC5FCC54594C0B2EAA23BCD0AECD748BAC98E6FBC
585AAD8E9C4EF0A988910953D75639F7665E1DA6E52C59FFD601DB0FC59516E1
D8CB587BAB8E0FCD86279D3A319CA9C96C6A06E0979AF303141B7072D877F76C
90A7AD75F70B9B68A93B7C3D3F5797631877E9E7E144C3B535F54090180933E8
DBB7892CC2749A54A9FC8CBDCA504836E79CE52C89135DE80774BBFAF804208E
BA005138F685068355C8EFA53699491A47A7ED903C365B7E440ACE0DEC417620
EB66E9EA0119DB1600A4FD5207D8B8A2EA550ADCFA2E2E32577EC55042F3696F
DE38A90E77A786C8380F43BF58744DB047631F51415EF2D7AAA29C14FB4FD6C6
65AFAA1677707772D0D56D4093FC63428A012D49AB8C61D504C0123A6505F693
8E5EE6E97DEFC6EFB1A961E6601F376692C152ABEC8C0F5E74093F8C20FE28C6
2B351F2D0E4D8842BAC8A82CF8C0DAA52DC00B89E9F9C9D1D4FD1B2155AA0CFD
F8D398AB22B6E996D5292244BDF6738FA1A9C46A454E4116C9B15F6D70D3DEEE
0C02809F5F15755CE43F8E11FB8734EE20F103C714D82EC626AA78F1A6D11BF2
F022829AB88CC9AD790E0BCA7D1FB41CA4736889D120B34E28E0A378D9913577
F9A2AF66BF9FD7AF4765EBFB1955B418862E1ABE5077FB663D171A81677BBCA0
783AB2D0C2F1A7EC451E423E721FDCB94FCC24F6805C96CF7DE209F64181F1C6
DA1F5087153DC79D0FE75F6D848DB686DF0ECF6A10DC02629A46DC8D14FDE4B6
AB8609F0F4A72C77B0341BEE84681CEC496A677777854B9CEB6595110CDCA552
0699E03D939923E2E0E673467DDE0D95DE117658514ECE2CD6E47245C27D6262
42DF532BB56F5607AD212DEE4A3D00358302671F7D7CE64F171E32EC686974B1
42E55718844A35130B13784EF7BD374E2C259D9ADE47527A16FA688B6D6BC56F
2E6498F919D8B514C99CFE51AE45FB9F5B547529058B6A7801B7754C23DCE63C
C5F3759CFC7AFA38A25B5BCC747B54317DEB7465C2E2C55988811076C7DD921E
CEC322F35F7C7B2AC060E9E83E39A0CA0460A3D67F8A0484C4D487B4A235A564
A9862060C676542A710AE95B8A26241F56B9880677154983A547547345C5BAC9
5624DB3C3BC95093DE6D7BA4153C637CC8586E88F2A72E4D471FCCB64133A397
EA1456DA1FC49FC66D11F478200068481A26E4825B75271BF738671F0242B3AE
F88FB8EF0087FF2D2E971C1945B846E84D7D4BFD7BCDE69D96A62BF98723F685
7EE4D713DBA9283A565F2FDE7B78EC242AE5ACA60EC338BCA40CCE35E2C86EAA
FEC6547326DCF3F9F4D924C19403A01A63257A4B0519EE125B43B5466AA9D371
B705F56941A23051B16346C1443C0749A9F483B07685815271979C8593ED6635
8B2F42324F4D4042502D9C351D872F33746B59713478837115E8C7061B2EE477
541288AD177434C001A23881B104CAE5EB2C5A7116932E2E2916D0F39D6566C1
018FAF6D7EDF72A4C74E02AE79F9973AFBB9744E9104B8F9FAADA5501BF4B0F8
29DD95AFFE475C9328C340C050D10870FC3F46E8C3369C177A8FA5B19FA08C88
59752C60BC458C7EF6FD45090B2EBCE991EC709120ACF20D945DAF762AE65239
AF8A33A800F1669EBD9B12F448888ADAFEC5D146BC680C08A74B025D26D3FEDA
43DEDE0C03D57E1D1024F4837EBF5B060C5EE654C0AA75F5A97C676E138BFD9A
8F94FDF1CE89AF234520294797B2C365B424FD3CB85AB5A6687DBEE5093CFAFB
261282D3FD57D2B62DEF132BFF775BD7873361D1B33367341472EC99A6FF2EA4
AEE43CFB91F9E634B9A785C916FC1A4791FD4A44D4E1B66682373D539C6CE8F2
CD2D8B8973001F9B104195C7664A17E6D8072F117D773BEC8EC9D76EB4018E03
0D505563A35B9B7725ABA5AF057B72BD71BE68C7F34B35D16140ED18C942E4A4
6BEB4C2B128C9A0B9B1FCC53D4EB7DD0BB317B5018BD03B7E0AB0F944AE299DD
BBCB88FC7FB9E170B16BF4F584EC1B2AA7F21C2E5881E2DA71E81B3E02740F43
20952D7FD2C1F9AF7CBC2B3C764419F6A260EF38EBCCD24B55142B5C5E074FEF
5810F43686E0E747ED36E69DAEE0F7D001A5982B52A55B4CDC71BEBF54F42A54
1F3C3510CEA9D9C94335FCD2CEA7D352DFF720B9062207AE31CC6D0EE041AEEC
EF2DAA57776CD85F48FE763972CF7DC886CCB8CBF9BAE26CAB55A3D02D7C787B
8A5E542F550CA2751E2F8252A26D8DE3D3FEDA40214C543203ED87C3160D4C7C
ACAEF9BFE5BA579D53DF15D2BCE35FB648952565EB2C33AD73B34C3DA97851B9
77E25C3A0D3D59FEC9F5170683FFD486701D6F69E70AAA2BB49EDCE1AD7545A3
E0A394B2E287DA5675CC6AEA53883CCE42399E61EFEFECCBBF1CDC7333BA7F3B
BFF17C39C649D57C154A7580814BA71C35D706D0A264AACD3D06ECE7B166667D
6A6E16137A22FCB8044EFEB5C4FD8EF20C07FB1CF10ABEAC218D4C590B480B39
5CD2DBC31B9C3113449D2CF707E621D943176B865DDB6446FD4502F040E69344
D8F57C817B402DBDA95E15AE0241E337EC9F5D654910972D805C9C39E9C68515
CED66F5DBAE8051B75790C7CB6DE7D942AA5F8E48CF4A229E954A7A762BF90E6
957EE0F46784684732EA938F46EDBE725396CAA1A3387566A7EFA8831B7B5283
87F125A135E82BA8E445B0E13E23D279234ECF07BB619DF0D12813BA03964311
C825FB6D0555891D380111C9CF390DE215CE574A94C85709D8F35968AAB31E39
FF6A4F597B3AA9A50AF4705ED64DD88BBD79A83D510BE61635FFAE5DB1CC1700
48B6A69658450227D10F7594C8503A2C71F40A73154E659F964559E97B4AE707
EF7489E8E6BDB7ADA047AF6A52FAD86ED46B1C09BEC773A1B7F12EB613CFB442
BAE77908FB80B926E5BE45F878C2FCCC070AA15EE25AC7603C32BEA1F414FAA8
0D25B22FA37D777615DCF57EB7075FF3229A2C27E84DC758EF6E5D17A1E3B2B8
39E1BD1D2B68A4B1D321195F22F136A6B8139AA2124E404381DDF72B01EC2179
1BA5FB0A663C773FFB7024F16FD9578B74B5FA06AEA231C8D59EEEDF19840508
DD4F9C561EF9DD3BE97E9BCD1A270AE8A9737526C0D3E6EABDC312F1393A0E85
F5330AFB1D6B74DB6BF0D6DCE5CC646112D7D82F1275268F64ED0FAAF44E082F
26635FCEA44A8B65AD694F3CB0767D94F0379F2AE275116CA9EA956B23B49433
F9206AD2E2E9919EA959AE758C38C3645EDB965373F6B41D6DE50431F3E3337F
BC1FBC63C05EEF1142BD4FEB6EB6E73C4964239CA319C1C76F48EA30FF25DA06
1A45BB209AC780DEF9B56C36785EF6EC525221F77094013B5E067EBF1A06B3F6
CFE9F3C3F9CD44C49A57B3955FE658D9F085E71AAE8B6F2BE5F214A26E64F549
BE27AADDA16273F96566E18E12601AF5D8EFD0874D24CB5E545E7674626C9BBF
D0A7701FB6ECFC9D11186160DFFD0A07045FC18B7803551340DAC294B7781F8B
5777FE26902D61029C9FC78638B499FA478B84FFE0DEBBA9B8CA5911407BB93F
12C959B1453055230105E3FBD8574EF7DC724EE2A803AEA4B73CC9FDDAA8DBB5
BB67BE887E16729069EC027472C8ACB9B8D5DDD9B0CAF7DDC3188FDB4F7258BF
8FF72EA3CB503935DE65D549DCDA0DD0898DE5364E638CFCD1E4C432DCB85A4C
6F51E295F6CF0299ED59134D1EFA43AC7E16AA90D46E085D18C53A96C4BD719E
BDEFA46C42DD905D6277390E5CD646C37DB98899B0D73834C46290455A2EDF34
0541D470DD1F2C3B6761483E1F26D2CE3FDF0514EBB30414806204713A0469C0
B2B9D7C8D006EEC36C6E77EB1FDD5C8B1C854DE5D6708E210BD63DB177704AEE
AD595326938181AA0C57662F2F10370509659CA0C913D25944254F7B6C7FE9BC
151200A335ABDBCFD4DCEF0826430438807C545FF2FAB63F92145E93C92A5BD9
AE9E41A8909CC39C2E7E4CC8D389819F06D0E11B18E71D65C350B0B69903C273
D9CC369FBAEE92C636AE37B0E60C2A3E707656C242383B1FBC374E61E82D01B6
26B315392F5CEA0619E2AB6DAFAEEA96F6B62D3336F0C199CD1CBFB3333EB29C
9321F5303B4674175C569A31A793C97176BFE6A2BC4455CFE44A171430B37F84
5BAA2F310047BDBEC111F33CE5795F0449E96F779E406D8A582165E073CFE690
387169DD226BBE7F1740664FBDA68ECE7D6BF5C7239F3A4598DFAEE489F1673D
6899D6E58A4E8205D9C53D9BE24D9593326A6CA8F4B2A49D3B2FB342630B513D
2A34F6ED991114EBA6B6F4EB063D81B7FDD7DB95735993051B2FBB6B5C889FF1
8812FA55E6732016FC8A3E97DF4572A4FFDE8EC2764E5DBF8BD0EDE5ED92F2CE
20EDB5C086C7A1AEE085C8718572E99BD7B08EB5C0318A9A04087A1DFAEA5AB5
AD3E4E74E9E258B08AADFF7BFD1F03427DF57A08609857D3D31C1CFE913E5C2C
199063F16E56C8A6FAF4DCD978F30354A174808A15480EE5A65CD9F6E427CE0C
8A1FF290A88D6A9D1EBEC97EF7492D6E933B557F10386BFD0F2CEDCF940DF67A
93DA0D733DB05CDDDA4E50422147C878C12A2F13CEFCA43971AA98F1349CFF81
082D85D2A44C606953E9486478E22CC875A7A3D2071464F330CD78FC7776CD59
EE369E266F7FEBBDD17E7A59CA1BF966232FCCDA3CA15A9D206513727CCA7F0A
EF332FF4736591A8155CFF6CAACBAAC09FF31E674D7D60124C35394617050C06
E193954427AB3826424D4F381DDA31A50658E614810C5098AEFF5BDC371EF316
F3DD748052084DD08A2FB5B3EFE35F48B3F595FBEFB8A6EF02C80D13D745876C
8417A79B7D4157A41376F86BA29B22DCCC6BC49496B57331CCF13BF612A440A9
48D54C580D595B482D7FE8C1215B696550C0AF6BBD8117D24F65434278ED1E2B
125F1916C69D36E22CDC050B5B6ACB17B3A6B67B011E73F61E000B08D9BA416C
60113838DAFBD62B1BB8CF9D3C404563C645738B55718122B24FC5FD78F9DD5F
2CBC15C3D8F37C965F7BF91D8330A4ED04CCFF03D962E6207D0E89DAF77FFCED
767807A60AAC57D822E13B10567B8214F835586DE117BAC7D9688CB468DF543C
AA3FDD53657431B25BD77425DC0150EF97A80810FACBE7E538F535F622BE2DE4
ADE0FB24E11BA0CE9FB81033F4985D5EFD534FD8D00421B50CB0146827ECB6FC
A1EC94CDB17ACB917926896E324C1CD3BC5C85320B607E11FA48F32226762147
C400F275B59A862A2A61551D25FB54702C71FA7E4C9576FE11B2C183A69F2DCD
87A7414BB69174A2343B583911D695A3CEC10A29814E9192D4F502A56DAEDB2E
DA48690F0D7D6F60B11AAA23D3BAECD6246886D863D9B379BD9FBCD3940ED883
4D6C3CDAB31F07DA5CF015B003CED4FB45118EC1D54864B75193D7FAB5D407DE
DA98EF88D47D89DC56AFB5B1A44C76430269C6F3F9164053869B884C7F9D2312
8D8D55AFECC4948652BD450D3FEB7860C0DE029CE64666855BD40665424CF0B3
5460FF5074C09686F3B1A15C5B7F6B66CB1C33F7051E35B6DADD96BDDBB91BC8
9DD49087ED999A23BC6EC7A20E7D47B70D9EA877F52491A388753B4007C547D7
3C9CF39509098C0BAF7037A43DADA49C8E993C3F1EE896BB94ABF655DA4DA390
E95AC4F06FABEF4DAA369B6F4D9F443A48AE04B6CB1328CAB97970CB8A1A5EC0
EE856A533E6FBD05FEDF2A16E39955CDF0A3639B593042468098604124A0A455
4D82B797D227D1AE8141CACFDC36AEFBD16F5012841D9A41318DA80BBC31A682
3FDC51147805A43EC377
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: MSBM10
%!PS-AdobeFont-1.1: MSBM10 2.1
%%CreationDate: 1993 Sep 17 11:10:37
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 67 /C put
dup 78 /N put
dup 81 /Q put
dup 82 /R put
dup 84 /T put
dup 90 /Z put
readonly def
/FontBBox{-55 -420 2343 920}readonly def
/UniqueID 5031982 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMTI10
%!PS-AdobeFont-1.1: CMTI10 1.00B
%%CreationDate: 1992 Feb 19 19:56:16
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-163 -250 1146 969}readonly def
/UniqueID 5000828 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMBX10
%!PS-AdobeFont-1.1: CMBX10 1.00B
%%CreationDate: 1992 Feb 19 19:54:06
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-301 -250 1164 946}readonly def
/UniqueID 5000768 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR9
%!PS-AdobeFont-1.1: CMR9 1.0
%%CreationDate: 1991 Aug 20 16:39:59
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-39 -250 1036 750}readonly def
/UniqueID 5000792 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMSY6
%!PS-AdobeFont-1.1: CMSY6 1.0
%%CreationDate: 1991 Aug 15 07:21:34
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-4 -948 1329 786}readonly def
/UniqueID 5000816 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR6
%!PS-AdobeFont-1.1: CMR6 1.0
%%CreationDate: 1991 Aug 20 16:39:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-20 -250 1193 750}readonly def
/UniqueID 5000789 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMI8
%!PS-AdobeFont-1.1: CMMI8 1.100
%%CreationDate: 1996 Jul 23 07:53:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueID 5087383 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR8
%!PS-AdobeFont-1.1: CMR8 1.0
%%CreationDate: 1991 Aug 20 16:39:40
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueID 5000820 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueID 5000793 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMTI9
%!PS-AdobeFont-1.1: CMTI9 1.0
%%CreationDate: 1991 Aug 18 21:08:07
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTI9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-35 -250 1148 750}readonly def
/UniqueID 5000827 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMSY8
%!PS-AdobeFont-1.1: CMSY8 1.0
%%CreationDate: 1991 Aug 15 07:22:10
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
/UniqueID 5000818 def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964
7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4
A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85
E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A
221A37D9A807DD01161779DDE7D5FC1B2109839E5B52DFBB2A7C1B5D8E7E8AA0
5B10EA43D6A8ED61AF5B23D49920D8F79DAB6A59062134D84AC0100187A6CD1F
80F5DDD9D222ACB1C23326A7656A635C4A241CCD32CBFDF8363206B8AA36E107
1477F5496111E055C7491002AFF272E46ECC46422F0380D093284870022523FB
DA1716CC4F2E2CCAD5F173FCBE6EDDB874AD255CD5E5C0F86214393FCB5F5C20
9C3C2BB5886E36FC3CCC21483C3AC193485A46E9D22BD7201894E4D45ADD9BF1
CC5CF6A5010B5654AC0BE0DA903DB563B13840BA3015F72E51E3BC80156388BA
F83C7D393392BCBC227771CDCB976E9330253244EE95F3B511D933DFE05D868D
876A8553993B0FEDC9A514CB2BDAFA0C223266B2C8BC230447A30844DAAC3CC8
5CBA57883A2A135693189583426D25E2EFFF292BF6CE4537496D1851B4DA4AEB
A7265D68F39633287061E62E88F359A92410DE9777A00B12DFC77A498371BACD
E22A8EF3416C1D56963402CE4993A3033ECECC753D8A5E82AB552E5D94EB9C31
56C6D12DB4F2A94E7F3D3BF53D87EF89D2B914F8538C87F0893ACCB2706F80AF
5BB0A63A6CCFDC0D02B0FD5F15181737EA0210A3BE137F524EA3077888F41516
3D722529B89181AFED1CB250C6B4C36A286B89530488B6849B69AD0CD4340515
79883D200861E833687E5028ACB310BE54E60CB69FD4BE762BAA582C9EE8BFC6
2432D52A1B13D1E8AB336FCAD98318C248C4670E9D73DB091E7E1F72ADAEC59E
1DF3F29EB3DAA2C4334902292FDF13FB45CBC7F89815BFD455B90D6316614744
DBD718C3567CDCDB92ABAEF32F7379506ED619E7795C9BF20620D00DB1E09FA4
DCA6FF8D40851CAF3A2981D96117D5D77E9626135B36CDA1391A7E25D6D69CF8
E9EE647D32B5D7D1355D1C3313AA0AADCF866DB83AE54D211EB8DCF0828B3A4C
31053626370BD468B1ECBCE27D11ABFC7779DEF40319755222BD87C929E0D4DB
5D77714DE6F278E5953E2A260F8B130A86C494D72C314B404CF1E41C78FE73B5
418DE75AD313D53515A6F3B551BC1B374F464D99D3B8C31FF6375142A267719C
70161CD7E0AAE8B137518A0FF8744A1B042051D8A658A8FC95252C9ADF60A70C
4F5EB709543946AF0DDF9600E13C7012F901AF5149ACEAE89A0EA1D1C657C773
0254BC8C7CB72CE15014BD618B14E30C7611194D969CF0ECDECDC95FD38E6F27
6FE9EAC519CFCA9D726A2CF62951D21322D4FEA3DFC7AE7FE5AC7B5B2BD05E00
A6D68DFC45B893A1AC9E083E895D92926077B3424A79B47BD34B79683544A8F3
C4B2B3E0366A6C28C75E56F06A6899973188AFD8F04B7F43D19DB1F8D1B14CA5
462590C918EA440A3A54ADAF9C7525380D7778445900B4CA2ACC1676924A6AFD
A2DBDD6BA0A5B2519422E4160DFC6C78CEA9B90DFB089657BE7D113D2B486AAF
0A0BABF7E437A8467AD7F994919214E8B0E7D37B1D328AB4750A134A9233F013
BE8618FD50A705821CCB017373875F7C8E9621ADAAE509B42811B6D6E9979512
60BDCD8F5F3E809A472127084ACCFD55AC4F4444D839840BCD5B348CF1218F5E
ECC60543D94EA5291D4982D6AAA52181930D0DC6277E18F024E026CFD5C95BDC
BB8C2C86DF0F84220088FD61B0B2691DFC8A5919EADF4788484A0DC90024788A
04DC8C3C2136FEAA310FB8200AE796D2B9F3B933D6F2C4132AE6E039CB531377
FC8ECB56CE79A13A99FA23FAD84F5106833E2BE5C8FE79787CF374860FD82A66
21D71E17F31103CB15331372E2B5F3DBB84DB3D06E2CAA8CAE26ED8438CCAB96
8DCEBF4F250590DEA648D93A191DB3C4569470923AEC320D4CE7F9C40EF03D37
B0D2DEB968E961AC5BAA13400B08EEAF1B6DB9CF03A9B3D589678E922B38B07C
C0A774F056561C83E21F9E20485FCBBF7DCA6A3997CBF52BD54C2D68A05463B1
330DF2C166DE0D7B8E8DA74970BCA92574E248377ED1DEBB88BC39FAEE9A7D11
BE75A4A14ED1F360FE9A8E5DF3D07EECE847FDB2CD84A122C53A8624EC2E48E1
30ECE4893B750AD0C799FC7690C53A25EF33753937E651A77809340F1DEAAED0
016E3A28DDDF5193F9BD0F9C4E74C19BF7D94857F71F94A28D82563BB647C7D0
8139BBA5AF553B4C84B11CE018B93B6FACF9BBF6A73A89299D508890B497E8D6
A115DC8E11781B650A3C0604125AC2BC6FDC499905F7BFC9FEEB18A786D5D4E0
890C17F191DCB37A376B31A7F8A00D83FFC19FAEFF983AC7D1FAE6321B8C92B2
0251FB952C20288516D77E845E1002C54789BDF6B2D338D1914B953C876994CC
830E01A95711DE579D99783813F871E06CECB33816C34B0E7661ADD77BCBC018
6B444CAAC015EF3ACC066289CD51D34F7BE1DC761E9E76AD3C8FDAEEAFDFA32A
ED193A98F2860C68011953184FAE9256591DDFB2D0BF89A4867813D17FE916E6
395DB91442C84E0A8F103C3DAC2C630CD57A9B81C02DAD4B7345F6FF6D34D15E
AD8CEFB0E31567D0548C1236FD67F1E0C767DC1FC8B76C5798CB1A18F43CA8E6
955269552ACC4AFF70675599A16A1F8AC9D1BD71ED0EDD5ABAD6EFF16F206094
98F091AF1A6FE7D0690379EC4673C642C66D66015E3AD801A95AB95028573CE8
711DB779F8AEFFC7964C25BB2A7E2C0C6AEFEE9773C801BC3231956B57828188
9E60E273CB13180F1C1F2C36EFC9AF647DAD8808D59EE09417BCE4B2C550BA2E
9B2C82502441568B74BD4B2DCAA3A5DBE516554669647EBF2E
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR12
%!PS-AdobeFont-1.1: CMR12 1.0
%%CreationDate: 1991 Aug 20 16:38:05
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-34 -251 988 750}readonly def
/UniqueID 5000794 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR17
%!PS-AdobeFont-1.1: CMR17 1.0
%%CreationDate: 1991 Aug 20 16:38:24
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR17) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR17 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-33 -250 945 749}readonly def
/UniqueID 5000795 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
TeXDict begin 39158280 55380996 1000 600 600 (ode.dvi)
@start /Fa 206[33 49[{ TeXf7b6d320Encoding ReEncodeFont }1
58.1154 /CMR7 rf /Fb 252[34 3[{ TeXbbad153fEncoding ReEncodeFont }1
58.1154 /CMSY7 rf /Fc 151[48 31[69 65 53 70[{
  TeXaae443f0Encoding ReEncodeFont }4 83.022 /CMMI10 rf
/Fd 134[59 2[59 62 44 44 46 2[56 62 93 31 2[31 1[56 34
51 1[50 62 54 14[84 9[88 1[70 1[86 2[85 12[56 56 56 56
2[31 46[{ TeXf7b6d320Encoding ReEncodeFont }27 99.6264
/CMBX12 rf /Fe 165[39 5[39 84[{}2 58.1154 /MSBM7 rf /Ff
137[31 2[29 29 9[36 3[32 20[47 48 9[50 8[19 30[29 4[31
37 1[36 5[28 14[{ TeXaae443f0Encoding ReEncodeFont }14
49.8132 /CMMI6 rf /Fg 143[83 55 55 7[83 46 1[83 46 7[46
1[120 22[73 73 1[74 1[74 1[74 1[74 6[73 73 6[67 67 4[48
48 66 66 4[62 62 4[44 44 61 61 50 50 3[28 10[38 38{}34
83.022 /CMEX10 rf /Fh 165[55 5[55 1[60 65 2[60 10[60
67[{}6 83.022 /MSBM10 rf /Fi 133[37 44 42 60 42 49 30
37 38 42 46 46 51 74 23 2[28 46 42 28 42 46 42 42 46
6[56 2[91 68 68 65 51 66 70 62 70 1[82 57 1[48 35 68
1[59 62 69 65 64 68 6[28 3[46 1[46 46 46 46 2[28 33 28
2[37 37 1[70 18[46 4[80 1[51 56 11[{ TeX74afc74cEncoding ReEncodeFont }
61 90.9091 /CMTI10 rf /Fj 134[55 55 3[41 1[43 1[58 52
58 87 29 55 1[29 58 2[48 3[51 9[108 2[73 1[78 2[79 82
99 63 82 3[82 1[69 80 76 1[79 7[52 52 52 52 52 52 52
52 52 52 1[29 33[58 12[{ TeXf7b6d320Encoding ReEncodeFont }39
90.9091 /CMBX10 rf /Fk 134[41 1[55 1[43 30 30 30 1[43
38 43 64 21 41 23 21 43 38 23 34 43 34 43 38 7[58 4[55
43 2[52 1[58 6[60 50 52 1[55 1[58 60 5[21 1[38 38 38
3[38 38 38 1[21 26 3[30 30 40[{ TeXf7b6d320Encoding ReEncodeFont }44
74.7198 /CMR9 rf /Fl 207[18 26[48 17[32 48 1[48{
  TeXbbad153fEncoding ReEncodeFont }5 49.8132 /CMSY6 rf
/Fm 194[47 10[30 30 30 4[47 1[24 24 40[{
  TeXf7b6d320Encoding ReEncodeFont }7 49.8132 /CMR6 rf
/Fn 137[34 1[25 33 32 3[43 62 21 37 29 24 41 34 2[36
31 1[37 10[41 1[41 5[56 1[48 60 10[37 1[55 35 1[20 20
18[46 26 36 59 1[33 1[46 44 2[31 40 36 41 1[35 42 41
41 1[33 2[29 31 36 40 45 11[{ TeXaae443f0Encoding ReEncodeFont }46
66.4176 /CMMI8 rf /Fo 137[37 20[35 35[55 5[35 35 35 35
35 35 35 35 4[55 1[27 27 29[51 1[51 2[53 5[{
  TeXf7b6d320Encoding ReEncodeFont }17 66.4176 /CMR8 rf
/Fp 134[45 52 65 44 52 33 43 41 41 1[44 55 80 27 47 37
31 52 43 45 42 47 39 39 48 6[62 53 75 86 53 62 53 56
69 72 1[69 73 88 62 77 50 40 76 71 58 67 75 65 1[68 48
1[71 45 71 25 25 18[59 33 47 75 54 42 57 59 57 54 1[40
52 47 52 40 45 55 53 52 1[43 45 40 37 40 47 51 58 11[{
  TeXaae443f0Encoding ReEncodeFont }81 90.9091 /CMMI10
rf /Fq 135[40 2[61 61 1[76 3[45 3[25 35 35 45 45 7[61
9[50 55 2[63 9[65 14[0 0 3[61 91 10[91 2[45 1[91 6[71
4[71 71 1[71 71 2[45 11[71 25 71{ TeXbbad153fEncoding ReEncodeFont }31
90.9091 /CMSY10 rf /Fr 138[75 52 53 55 1[75 67 75 1[37
2[37 2[41 61 75 60 1[65 14[100 101 7[50 7[102 13[67 67
67 3[45 45[{ TeXf7b6d320Encoding ReEncodeFont }22 119.552
/CMBX12 rf /Fs 134[40 1[55 1[45 28 34 35 1[42 42 47 1[21
1[25 25 42 2[38 42 38 38 42 13[47 5[74 1[64 7[59 1[62
18[25 33[47 12[{ TeX74afc74cEncoding ReEncodeFont }25
83.022 /CMTI10 rf /Ft 134[44 44 60 44 46 32 33 33 44
46 42 46 69 23 2[23 46 42 25 37 46 37 46 42 11[62 3[65
4[52 2[30 62 1[54 2[60 59 62 8[42 2[42 42 42 42 42 2[23
28 23 29[69 5[60 8[{ TeXf7b6d320Encoding ReEncodeFont }43
83.022 /CMR10 rf /Fu 139[37 38 39 14[42 53 46 31[72 65[{
  TeXf7b6d320Encoding ReEncodeFont }7 83.022 /CMBX10 rf
/Fv 128[45 45 2[45 40 48 48 66 48 51 35 36 36 48 51 45
51 76 25 48 28 25 51 45 28 40 51 40 51 45 25 25 1[25
1[25 56 68 1[93 68 68 66 51 67 71 62 71 68 83 57 71 47
33 68 71 59 62 69 66 64 68 3[71 1[25 25 45 45 45 45 45
45 45 45 45 45 45 25 30 25 71 1[35 35 25 5[25 13[45 45
3[76 51 51 53 66 71 66 2[68 1[63 71 2[{
  TeXf7b6d320Encoding ReEncodeFont }92 90.9091 /CMR10
rf /Fw 134[37 2[35 41 25 31 32 1[39 39 43 63 20 2[24
39 35 24 35 39 35 35 39 11[57 55 43 56 1[52 1[57 69 2[40
30 5[55 1[57 8[39 2[39 1[39 39 39 39 1[24 1[24 4[24 39[{
  TeX74afc74cEncoding ReEncodeFont }40 74.7198 /CMTI9
rf /Fx 149[20 27 27 53[47 71 19 14[71 12[55 16[35 55
20 55{ TeXbbad153fEncoding ReEncodeFont }12 66.4176 /CMSY8
rf /Fy 133[43 4[54 5[49 54 81 3[27 1[49 1[43 54 2[49
13[54 8[50 1[73 46[49 25[{ TeXf7b6d320Encoding ReEncodeFont }14
99.6264 /CMR12 rf /Fz 134[70 2[70 73 51 52 51 70 73 66
73 111 36 2[36 73 1[40 58 73 58 73 66 15[103 8[99 5[94
20[43 45[{ TeXf7b6d320Encoding ReEncodeFont }24 143.462
/CMR17 rf end
%%EndProlog
%%BeginSetup
%%Feature: *Resolution 600dpi
TeXDict begin
%%PaperSize: A4
  end
%%EndSetup
%%Page: 1 1
TeXDict begin 1 0 bop 330 701 a Fz(Quasi-p)t(erio)t(dic)43
b(solutions)f(and)i(stabilit)l(y)d(of)i(the)h(equilibrium)517
884 y(for)e(quasi-p)t(erio)t(dically)g(forced)h(planar)g(rev)l(ersible)
g(and)550 1066 y(Hamiltonian)f(systems)g(under)i(the)g(Bruno)f
(condition)1137 1319 y Fy(Heinz)33 b(Han\031mann)131
b(and)f(Jianguo)32 b(Si)2736 1283 y Fx(\003)1191 1435
y Fw(Mathematisch)d(Instituut,)g(Universiteit)f(Utr)l(e)l(cht)1077
1504 y(Postbus)h(80.010,)f(3508)g(T)-6 b(A)28 b(Utr)l(e)l(cht,)h(The)f
(Netherlands)1187 1620 y(Scho)l(ol)g(of)f(Mathematics,)i(Shandong)g
(University)1050 1689 y(Jinan,)e(Shandong)i(250100,)f(Pe)l(ople's)g(R)l
(epublic)g(of)f(China)1593 1887 y Fv(4)k(No)m(v)m(em)m(b)s(er)g(2009)
392 2322 y Fu(Abstract)p Ft(.)59 b(In)35 b(this)g(pap)r(er)f(w)n(e)h
(in)n(v)n(estigate)e(the)i(existence)f(of)h(quasi-p)r(erio)r(dic)e
(solutions)h(of)392 2422 y(non-autonomous)17 b(t)n(w)n(o-dimensional)f
(rev)n(ersible)h(and)h(Hamiltonian)h(systems)f(under)g(the)h(Bruno)392
2521 y(condition.)35 b(As)23 b(an)f(application)g(w)n(e)g(study)g(the)h
(dynamical)f(stabilit)n(y)g(of)g(the)h(trivial)f(solution)g(at)392
2621 y(the)28 b(origin)e(of)i(a)f(quasi-p)r(erio)r(dically)e(forced)i
(planar)f(system.)37 b(Under)27 b(a)g(mild)h(non-degeneracy)392
2720 y(condition)21 b(w)n(e)f(giv)n(e)g(a)g(criterion)g(that)h(is)f
(necessary)f(and)i(su\016cien)n(t)f(for)g(a)h(large)e(class)h(of)g
(systems.)392 2920 y Fs(AMS)30 b(Subje)l(ct)f(Classi\014c)l(ations.)39
b Ft(58F13,)26 b(34C25)392 3057 y Fs(Keywor)l(ds)42 b(and)e(phr)l
(ases.)74 b Ft(Quasi-p)r(erio)r(dic)37 b(solutions,)42
b(stabilit)n(y)d(of)g(the)h(equilibrium,)i(Lia-)392 3156
y(puno)n(v,)27 b(Hamiltonian)h(system,)f(rev)n(ersible)f(system.)165
3542 y Fr(1)135 b(In)l(tro)t(duction)165 3745 y Fv(W)-8
b(e)44 b(are)g(concerned)f(with)g(quasi-p)s(erio)s(dic)g(solutions)h
(and)f(stabilit)m(y)i(of)e Fq(f)p Fp(I)54 b Fv(=)47 b(0)p
Fq(g)d Fv(for)f(the)g(non-)165 3858 y(autonomous)30 b(system)h(of)g(t)m
(w)m(o)g(di\013eren)m(tial)h(equations)1175 4039 y(_)1154
4062 y Fp(I)g Fv(=)25 b Fp(R)q Fv(\()p Fp(I)7 b(;)15
b(';)g(t;)g(a)p Fv(\))p Fp(;)133 b Fv(_)-49 b Fp(')25
b Fv(=)g Fp(a)c Fv(+)f Fp(Q)p Fv(\()p Fp(I)7 b(;)15 b(';)g(t;)g(a)p
Fv(\))p Fp(;)804 b Fv(\(1.1\))165 4267 y(where)40 b Fp(a)h
Fv(is)g(a)g(one-dimensional)h(parameter)f(and)g Fp(R)q
Fv(\(0)p Fp(;)15 b(';)g(t;)g(a)p Fv(\))45 b(=)e Fp(Q)p
Fv(\(0)p Fp(;)15 b(';)g(t;)g(a)p Fv(\))45 b(=)d(0.)73
b(F)-8 b(urther-)165 4380 y(more)33 b Fp(R)h Fv(and)f
Fp(Q)g Fv(are)h(real)g(analytic)h(in)e(all)i(v)-5 b(ariables)34
b(and)f(quasi-p)s(erio)s(dic)g(in)g Fp(t)g Fv(and)g Fp(')h
Fv(with)f(basic)165 4492 y(frequencies)d(\012)696 4506
y Fo(1)761 4492 y Fv(=)25 b(\()p Fp(!)949 4506 y Fo(1)988
4492 y Fp(;)15 b(!)1085 4506 y Fo(2)1140 4492 y Fp(:)g(:)g(:)h(;)f(!)
1358 4506 y Fn(N)1414 4515 y Fm(1)1452 4492 y Fv(\))31
b(and)f(\012)1761 4506 y Fo(2)1825 4492 y Fv(=)25 b(\()q
Fp(!)2014 4506 y Fn(N)2070 4515 y Fm(1)2104 4506 y Fo(+1)2198
4492 y Fp(;)15 b(!)2295 4506 y Fn(N)2351 4515 y Fm(1)2386
4506 y Fo(+2)2495 4492 y Fp(:)g(:)g(:)h(;)f(!)2713 4506
y Fn(N)2769 4515 y Fm(1)2804 4506 y Fo(+)p Fn(N)2915
4515 y Fm(2)2954 4492 y Fv(\),)30 b(resp)s(ectiv)m(ely)-8
b(.)306 4605 y(In)25 b(the)h(analysis)h(of)f(dynamical)g(systems,)h
(the)f(searc)m(h)g(for)g(equilibria)g(and)g(their)f(stabilit)m(y)j(is)e
(one)165 4718 y(of)35 b(the)f(\014rst)g(tasks)h(to)g(b)s(e)f(carried)h
(out,)h(since)f(they)g(organize)h(the)f(phase)f(\015o)m(w)h(to)g(a)g
(large)g(exten)m(t.)165 4831 y(Determining)f(the)f(stabilit)m(y)h(of)f
(the)g(equilibrium,)g(in)g(general,)h(is)f(not)g(an)g(easy)g(task)h(as)
f(it)g(usually)165 4944 y(requires)22 b(\014nding)f(a)i(Ly)m(apuno)m(v)
g(function.)38 b(The)22 b(theory)h(for)f(linear)h(stabilit)m(y)i(is)d
(w)m(ell)i(established)f(and)165 5057 y(easy)32 b(to)g(apply)-8
b(,)32 b(whence)f(the)h(\014rst)f(step)g(in)g(analysing)h(stabilit)m(y)
h(within)e(a)h(nonlinear)f(system)h(is)f(to)p 165 5136
1418 4 v 267 5190 a Fl(\003)303 5222 y Fk(Corresp)r(onding)22
b(author.)33 b(This)22 b(w)n(ork)f(w)n(as)g(partially)h(supp)r(orted)e
(b)n(y)g(the)h(National)g(Natural)g(Science)g(F)-6 b(oundation)165
5313 y(of)26 b(China)g(\(Gran)n(t)g(No.)34 b(10871117\))29
b(and)c(NSFSP)g(\(Gran)n(t)h(No.)34 b(Y2006A07\))293
5404 y(E-mail)26 b(address:)35 b(sijgmath@sdu.edu.cn)27
b(or)f(sijgmath@y)n(aho)r(o.com.cn)1914 5691 y Fv(1)p
eop end
%%Page: 2 2
TeXDict begin 2 1 bop 165 337 a Fv(linearize)28 b(it.)39
b(If)26 b(at)h(least)h(one)e(eigen)m(v)-5 b(alue)28 b(has)e(p)s(ositiv)
m(e)h(real)g(part,)g(the)g(equilibrium)e(is)h(unstable)g(for)165
450 y(b)s(oth)35 b(the)g(linearized)i(system)e(and)g(the)h
(\(nonlinear\))g(full)f(system.)56 b(Unfortunately)-8
b(,)38 b(the)e(con)m(v)m(erse)165 562 y(is)k(not)g(true;)45
b(the)c(higher)e(order)h(terms)g(ma)m(y)h(destro)m(y)f(the)h(stabilit)m
(y)g(of)g(the)f(linear)h(part,)h(and)e(a)165 675 y(di\013eren)m(t)26
b(metho)s(d)e(m)m(ust)i(b)s(e)e(used.)39 b(When)25 b(the)g(v)m
(ector\014eld)i(is)e(p)s(erio)s(dic)g(in)g Fp(t)p Fv(,)h(the)g
(stabilit)m(y)h(dep)s(ends)165 788 y(on)34 b(the)g(eigen)m(v)-5
b(alues)36 b(of)e(the)h(P)m(oincar)m(\023)-43 b(e)36
b(mapping)e(of)g(the)g(linearized)h(system)f(and)g(the)g(stabilit)m(y)i
(of)165 901 y(the)30 b(p)s(erio)s(dic)g(orbit)g(of)g(the)h(full)e
(system)i(can)f(b)s(e)g(determined)f(b)m(y)h(v)-5 b(arious)30
b(p)s(erturbation)g(metho)s(ds.)165 1014 y(F)-8 b(or)30
b(example,)h(in)f(the)g(h)m(yp)s(erb)s(olic)f(case,)i(the)f(p)s(erio)s
(dic)f(orbit)h(of)g(the)f(full)h(system)g(is)g(not)g(stable.)41
b(In)165 1127 y(the)25 b(elliptic)i(case,)h(if)d(the)h(eigen)m(v)-5
b(alues)27 b(of)e(the)h(P)m(oincar)m(\023)-43 b(e)27
b(mapping)e(of)g(the)h(linearized)g(system)g(satisfy)165
1240 y(some)36 b(non-resonan)m(t)g(relations,)j(one)d(can)g(pro)m(v)m
(e)g(via)h(Moser's)f(t)m(wist)h(theorem)f(that)h(the)f(p)s(erio)s(dic)
165 1353 y(orbit)43 b(of)f(the)h(full)g(system)f(is)h(stable.)78
b(F)-8 b(or)44 b(a)f(detailed)g(description)g(see)g([11)q(,)g(18)q(,)g
(13)q(,)f(7)q(,)h(8,)g(12)q(])165 1466 y(and)38 b(references)h
(therein.)67 b(The)38 b(metho)s(ds)g(used)g(to)i(study)e(the)h
(stabilit)m(y)h(of)f(the)h(trivial)g(solution)165 1579
y(\()p Fp(x)p Fv(\()p Fp(t)p Fv(\))p Fp(;)15 b(y)s Fv(\()p
Fp(t)p Fv(\)\))43 b Fq(\021)e Fv(\(0)p Fp(;)15 b Fv(0\))42
b(when)e(the)g(system)g(is)g(p)s(erio)s(dic)g(in)f Fp(t)h
Fv(cannot)h(b)s(e)e(applied)h(directly)h(to)g(the)165
1692 y(quasi-p)s(erio)s(dic)22 b(case.)39 b(When)21 b(system)i(\(1.1\))
g(is)f(a)h(Hamiltonian)g(system)f(\(or)h(a)f(rev)m(ersible)h(one\))f
(whic)m(h)165 1804 y(dep)s(ends)30 b(on)i(time)h(in)f(a)g(quasi-p)s
(erio)s(dic)g(w)m(a)m(y)h(and)f(its)g(frequency)g(v)m(ector)i
(satis\014es)f(a)f(Diophan)m(tine)165 1917 y(condition,)27
b(Y)-8 b(u.N.)26 b(Bibik)m(o)m(v)h(in)e([2)q(])g(pro)m(v)m(es)h(the)g
(existence)h(of)e(quasi-p)s(erio)s(dic)g(solutions)h(of)g(\(1.1\))h
(and)165 2030 y(applies)j(it)h(to)g(study)f(the)g(stabilit)m(y)j(of)d
Fq(f)p Fv(\()p Fp(x;)15 b(y)s Fv(\))27 b(=)e(\(0)p Fp(;)15
b Fv(0\))p Fq(g)32 b Fv(for)f(the)f(Hamiltonian)i(system)1535
2277 y(_)-41 b Fp(x)25 b Fv(=)1702 2216 y Fp(@)5 b(E)p
1702 2256 126 4 v 1714 2340 a(@)g(y)1838 2277 y(;)122
b Fv(_)-41 b Fp(y)28 b Fv(=)d Fq(\000)2219 2216 y Fp(@)5
b(E)p 2219 2256 V 2229 2340 a(@)g(x)3521 2277 y Fv(\(1.2\))165
2525 y(with)30 b(frequency)g(v)m(ector)i(\012)1123 2539
y Fo(1)1187 2525 y Fv(=)25 b(\()p Fp(!)1375 2539 y Fo(1)1414
2525 y Fp(;)15 b(:)g(:)g(:)i(;)e(!)1673 2539 y Fn(N)1729
2548 y Fm(1)1768 2525 y Fv(\))30 b(and)g(Hamiltonian)i(function)1307
2785 y Fp(E)e Fv(=)1510 2724 y Fp(y)1558 2691 y Fo(2)p
1510 2764 88 4 v 1531 2848 a Fv(2)1628 2785 y(+)1745
2724 y Fp(x)1797 2691 y Fo(2)p Fn(n)p Fo(+2)p 1728 2764
257 4 v 1728 2848 a Fv(2)p Fp(n)21 b Fv(+)f(2)2015 2785
y(+)g Fp(F)13 b Fv(\()p Fp(x;)i(y)s(;)g Fv(\012)2458
2799 y Fo(1)2498 2785 y Fp(t)p Fv(\))165 3018 y(and)30
b(the)g(rev)m(ersible)h(system)1464 3131 y(\177)-51 b
Fp(x)21 b Fv(+)e Fp(x)1673 3093 y Fo(2)p Fn(n)p Fo(+1)1871
3131 y Fv(=)25 b Fp(f)10 b Fv(\()p Fp(x;)31 b Fv(_)-41
b Fp(x;)15 b Fv(\012)2307 3145 y Fo(1)2346 3131 y Fp(t)p
Fv(\))165 3298 y(\(under)30 b(some)i(reasonable)h(assumptions)d(on)i
Fp(F)44 b Fv(and)31 b Fp(f)10 b Fv(\),)32 b(resp)s(ectiv)m(ely)-8
b(.)46 b(Recen)m(tly)-8 b(,)34 b(Liu)d([9)q(])h(studied)165
3411 y(the)e(stabilit)m(y)i(of)f(the)g(equilibrium)e(of)i(the)f(rev)m
(ersible)h(system)782 3615 y(_)-40 b Fp(x)25 b Fv(=)g
Fp(a)988 3629 y Fo(0)1027 3615 y Fv(\()p Fp(t)p Fv(\))p
Fp(y)1178 3577 y Fo(2)p Fn(m)p Fo(+1)1391 3615 y Fv(+)20
b Fp(f)1527 3629 y Fo(1)1566 3615 y Fv(\()p Fp(x;)15
b(y)s(;)g(t)p Fv(\))p Fp(;)123 b Fv(_)-41 b Fp(y)28 b
Fv(=)d Fq(\000)p Fp(b)2260 3629 y Fo(0)2299 3615 y Fv(\()p
Fp(t)p Fv(\))p Fp(x)2454 3577 y Fo(2)p Fn(n)p Fo(+1)2647
3615 y Fv(+)20 b Fp(f)2783 3629 y Fo(2)2822 3615 y Fv(\()p
Fp(x;)15 b(y)s(;)g(t)p Fv(\))416 b(\(1.3\))165 3819 y(and)34
b(a)g(similar)h(Hamiltonian)g(system)g(using)f(Bibik)m(o)m(v's)i
(results.)52 b(In)33 b(the)i(presen)m(t)f(pap)s(er,)g(w)m(e)h(also)165
3932 y(assume)d(that)h(the)g(system)g(\(1.1\))h(is)f(a)g(rev)m(ersible)
g(system)f(or)h(a)g(Hamiltonian)h(system.)47 b(Motiv)-5
b(ated)165 4045 y(b)m(y)30 b(the)h(results)f(of)g(Bibik)m(o)m(v)j([2])e
(and)f(R)s(\177)-48 b(ussmann)28 b([16)r(,)i(17)q(],)h(substituting)f
(the)h(Bruno)e(condition)i(for)165 4158 y(the)j(Diophan)m(tine)h
(condition)g(w)m(e)f(construct)g(in)g(Section)h(2)f(a)h(family)f(of)g
(solutions)g(of)h(\(1.1\))g(whic)m(h)165 4271 y(are)c(quasi-p)s(erio)s
(dic)f(in)g(b)s(oth)f(the)i(time)g(v)-5 b(ariable)31
b(and)f(the)h(angle)g(v)-5 b(ariable)31 b(with)f(basic)h(frequencies)
165 4384 y(\012)231 4398 y Fo(1)308 4384 y Fv(and)37
b(\012)558 4398 y Fo(2)598 4384 y Fv(.)63 b(In)38 b(Section)h(3)f(w)m
(e)h(apply)f(this)g(to)g(study)g(the)g(stabilit)m(y)i(of)e(the)g
(equilibrium)g(of)g(the)165 4497 y(planar)d(system)g(\(3)p
Fp(:)p Fv(1\),)k(whic)m(h)c(has)g(b)s(oth)f(\(1)p Fp(:)p
Fv(2\))j(and)e(\(1)p Fp(:)p Fv(3\))i(as)e(sp)s(ecial)h(cases.)56
b(W)-8 b(e)37 b(\014rst)d(in)m(tro)s(duce)165 4610 y(some)d
(de\014nitions)f(and)f(notations.)165 4822 y Fj(De\014nition)35
b(1.1)46 b Fi(\(Bruno)41 b(c)-5 b(ondition\))42 b(L)-5
b(et)40 b Fp(\013)g Fq(2)e Fh(R)26 b Fq(n)g Fh(Q)39 b
Fi(and)i Fv(1)f(=)e Fp(q)2641 4836 y Fo(0)2719 4822 y
Fp(<)h(q)2870 4836 y Fo(1)2924 4822 y Fq(\001)15 b(\001)g(\001)41
b Fi(b)-5 b(e)40 b(the)h(main)f(de-)165 4935 y(nominators)j(of)f(the)f
(c)-5 b(ontinue)g(d)42 b(fr)-5 b(action)43 b(of)e Fp(\013)p
Fi(,)j(we)d(say)h(that)g Fp(\013)f Fi(satis\014es)h(the)g(Bruno)f(c)-5
b(ondition)165 5048 y(if)1610 5111 y Fx(1)1585 5136 y
Fg(X)1579 5317 y Fn(n)p Fo(=0)1737 5155 y Fv(log)17 b
Fp(q)1910 5169 y Fn(n)p Fo(+1)p 1737 5195 311 4 v 1848
5279 a Fp(q)1889 5293 y Fn(n)2082 5217 y Fp(<)25 b Fq(1)p
Fp(:)1914 5691 y Fv(2)p eop end
%%Page: 3 3
TeXDict begin 3 2 bop 165 337 a Fj(De\014nition)35 b(1.2)46
b Fv([16)q(])c Fi(A)f(c)-5 b(ontinuous)43 b(function)f
Fv(\010)g(:)g([0)p Fp(;)15 b Fq(1)p Fv(])43 b Fq(!)e
Fh(R)h Fi(is)g(c)-5 b(al)5 b(le)-5 b(d)43 b(an)f(appr)-5
b(oximation)165 450 y(function)33 b(if)306 562 y(1.)42
b Fv(1)26 b(=)f(\010\(0\))h Fq(\025)f Fv(\010\()p Fp(s)p
Fv(\))g Fq(\025)g Fv(\010\()p Fp(t)p Fv(\))g Fp(>)g Fv(0)33
b Fi(for)h Fv(0)25 b Fq(\024)g Fp(s)g(<)g(t)g(<)g Fq(1)p
Fi(,)306 675 y(2.)42 b Fv(\010\(1\))26 b(=)f(1)p Fi(,)33
b(implying)g(that)h Fv(\010\()p Fp(s)p Fv(\))26 b(=)e(1)33
b Fi(for)h Fv(0)25 b Fq(\024)g Fp(s)g Fq(\024)g Fv(1)p
Fi(,)306 811 y(3.)50 b Fp(s)473 778 y Fn(\025)518 811
y Fv(\010\()p Fp(s)p Fv(\))31 b Fq(!)f Fv(0)35 b Fi(as)h
Fp(s)30 b Fq(!)g(1)36 b Fi(for)g(any)g Fp(\025)30 b Fq(\025)g
Fv(0)p Fi(,)36 b(implying)g(that)h Fv(\010)2614 778 y
Fn(\025\026)2732 811 y Fv(:=)30 b(sup)2870 878 y Ff(s)p
Fl(\025)p Fm(1)3010 811 y Fp(s)3053 778 y Fn(\025)3098
811 y Fv(\010\()p Fp(s)p Fv(\))3290 738 y Fm(1)p 3287
750 38 4 v 3287 792 a Ff(\026)3368 811 y Fp(<)g Fq(1)35
b Fi(for)165 926 y(al)5 b(l)33 b Fp(\025)25 b Fq(\025)g
Fv(0)p Fp(;)15 b(\026)26 b(>)f Fv(0)p Fi(,)306 1070 y(4.)422
955 y Fg(Z)505 981 y Fx(1)505 1143 y Fo(1)595 1070 y
Fv(log)789 1034 y Fo(1)p 738 1049 139 4 v 738 1102 a(\010\()p
Fn(s)p Fo(\))896 1034 y Fn(ds)p 896 1049 69 4 v 897 1103
a(s)930 1084 y Fm(2)1000 1070 y Fp(<)g Fq(1)p Fi(.)165
1320 y Fj(Remark)35 b(1.3)46 b Fv(As)26 b(stated)g(in)f([16)q(],)i(the)
e(consequen)m(t)i(use)e(of)g(a)h(general)g(appro)m(ximation)h(function)
e(as)165 1432 y(de\014ned)19 b(in)h(De\014nition)i(1.2)f(mak)m(es)h
(man)m(y)e(of)h(the)g(necessary)g(calculations)h(simple)f(and)f(quite)h
(natural.)165 1545 y(While)29 b(condition)g(2)g(in)f(De\014nition)h
(1.2)h(is)e(unessen)m(tial)i(but)d(tec)m(hnically)k(useful,)d(the)h
(condition)g(3)g(is)165 1658 y(necessary)c(in)g(order)f(to)i(ensure)e
(that)h(the)g(set)g(\(2)p Fp(:)p Fv(25\))j(is)c(of)h(small)h(measure)f
(whereas)f(the)h(condition)h(4)165 1771 y(is)36 b(equiv)-5
b(alen)m(t)37 b(to)g(the)f(Bruno)f(condition)h(in)g(the)g(case)h(of)f
(the)g(plane.)57 b(This)35 b(equiv)-5 b(alence)38 b(and)d(the)165
1884 y(existence)f(of)e(an)g(appro)m(ximation)i(function)e(satisfying)h
(De\014nition)f(1.2)i(can)e(b)s(e)g(found)f(in)h([16)q(,)h(17)q(].)165
1997 y(The)f(Bruno)g(condition)h(is)g(necessary)f(in)h(man)m(y)f
(problems,)h(see)g([19)q(,)g(14)q(,)g(20,)g(3)q(].)47
b(Moreo)m(v)m(er,)35 b(as)e(an)165 2110 y(example)22
b(in)e([5)q(])h(sho)m(ws)g(the)g(Bruno)g(condition)g(is)h(strictly)g(w)
m(eak)m(er)g(than)f(the)g(Diophan)m(tine)h(condition.)165
2322 y(Throughout)29 b(this)h(pap)s(er,)g(w)m(e)h(write)762
2527 y(\012)25 b(=)g(\(\012)1050 2541 y Fo(1)1090 2527
y Fp(;)15 b Fv(\012)1196 2541 y Fo(2)1235 2527 y Fv(\))26
b(=)f(\()p Fp(!)1484 2541 y Fo(1)1523 2527 y Fp(;)15
b(!)1620 2541 y Fo(2)1659 2527 y Fp(;)g(:)g(:)g(:)i(;)e(!)1918
2541 y Fn(N)1974 2550 y Fm(1)2013 2527 y Fp(;)g(!)2110
2541 y Fn(N)2166 2550 y Fm(1)2200 2541 y Fo(+1)2295 2527
y Fp(;)g(!)2392 2541 y Fn(N)2448 2550 y Fm(1)2482 2541
y Fo(+2)2577 2527 y Fp(;)g(:)g(:)g(:)h(;)f(!)2835 2541
y Fn(N)2891 2550 y Fm(1)2926 2541 y Fo(+)p Fn(N)3037
2550 y Fm(2)3075 2527 y Fv(\))165 2731 y(and)30 b(assume)g(that)h
(there)f(is)h(a)f Fp(\015)h(>)25 b Fv(0)31 b(for)f(whic)m(h)g(\012)g
(satis\014es)h(the)f(Bruno)g(condition)1103 2935 y Fq(jh)p
Fp(k)s(;)15 b Fv(\012)p Fq(ij)26 b(\025)f Fp(\015)5 b
Fv(\010\()p Fq(j)p Fp(k)s Fq(j)p Fv(\))92 b(for)31 b(all)g(0)26
b Fq(6)p Fv(=)e Fp(k)29 b Fq(2)c Fh(Z)2530 2902 y Fn(N)2586
2911 y Fm(1)2621 2902 y Fo(+)p Fn(N)2732 2911 y Fm(2)3521
2935 y Fv(\(1.4\))165 3139 y(where)42 b(\010)g(is)h(an)f(appro)m
(ximation)i(function)e(as)h(de\014ned)f(in)g(De\014nition)h(1.2.)79
b(W)-8 b(e)44 b(use)e(the)h(inner)165 3252 y(pro)s(duct)806
3440 y Fq(h)p Fp(k)s(;)15 b Fv(\012)p Fq(i)26 b Fv(=)f
Fq(h)p Fp(k)1236 3454 y Fo(1)1276 3440 y Fp(;)15 b Fv(\012)1382
3454 y Fo(1)1422 3440 y Fq(i)20 b Fv(+)g Fq(h)p Fp(k)1650
3454 y Fo(2)1690 3440 y Fp(;)15 b Fv(\012)1796 3454 y
Fo(2)1836 3440 y Fq(i)25 b Fv(=)2010 3332 y Fn(N)2066
3341 y Fm(1)1996 3359 y Fg(X)1992 3540 y Fn(v)r Fo(=1)2137
3416 y Fv(~)2134 3440 y Fp(k)2181 3454 y Fn(v)2223 3440
y Fp(!)2280 3454 y Fn(v)2340 3440 y Fv(+)2452 3332 y
Fn(N)2508 3341 y Fm(2)2438 3359 y Fg(X)2431 3540 y Fn(\026)p
Fo(=1)2581 3416 y Fv(~)2579 3440 y Fp(k)2626 3454 y Fn(N)2682
3463 y Fm(1)2717 3454 y Fo(+)p Fn(\026)2818 3440 y Fp(!)2875
3454 y Fn(N)2931 3463 y Fm(1)2966 3454 y Fo(+)p Fn(\026)165
3686 y Fv(where)712 3799 y Fp(k)k Fv(=)c(\()p Fp(k)966
3813 y Fo(1)1006 3799 y Fp(;)15 b(k)1093 3813 y Fo(2)1133
3799 y Fv(\))p Fp(;)107 b(k)1347 3813 y Fo(1)1412 3799
y Fv(=)25 b(\()1545 3775 y(~)1543 3799 y Fp(k)1590 3813
y Fo(1)1630 3799 y Fp(;)15 b(:)g(:)g(:)h(;)1834 3775
y Fv(~)1831 3799 y Fp(k)1878 3813 y Fn(N)1934 3822 y
Fm(1)1974 3799 y Fv(\))p Fp(;)107 b(k)2188 3813 y Fo(2)2253
3799 y Fv(=)25 b(\()2386 3775 y(~)2384 3799 y Fp(k)2431
3813 y Fn(N)2487 3822 y Fm(1)2522 3813 y Fo(+1)p Fn(;)2636
3799 y Fp(;)15 b(:)g(:)g(:)h(;)2840 3775 y Fv(~)2837
3799 y Fp(k)2884 3813 y Fn(N)2940 3822 y Fm(1)2976 3813
y Fo(+)p Fn(N)3087 3822 y Fm(2)3125 3799 y Fv(\))165
4044 y(and)30 b Fq(j)p Fp(k)s Fq(j)c Fv(=)580 3931 y
Ff(N)628 3946 y Fm(1)564 3963 y Fg(X)566 4134 y Ff(v)r
Fm(=1)683 4044 y Fq(j)710 4020 y Fv(~)708 4044 y Fp(k)755
4058 y Fn(v)797 4044 y Fq(j)20 b Fv(+)950 3931 y Ff(N)998
3946 y Fm(2)933 3963 y Fg(X)934 4134 y Ff(\026)p Fm(=1)1053
4044 y Fq(j)1080 4020 y Fv(~)1078 4044 y Fp(k)1125 4058
y Fn(N)1181 4067 y Fm(1)1216 4058 y Fo(+)p Fn(\026)1318
4044 y Fq(j)p Fv(.)165 4337 y Fj(De\014nition)35 b(1.4)46
b Fi(A)h(r)-5 b(e)g(al)48 b(analytic)h(function)e(of)h(two)g(variables)
g Fp(f)61 b Fv(=)51 b Fp(f)10 b Fv(\()p Fp(t;)15 b(')p
Fv(\))48 b Fi(is)f(c)-5 b(al)5 b(le)-5 b(d)49 b(quasi-)165
4450 y(p)-5 b(erio)g(dic)45 b(with)f(fr)-5 b(e)g(quencies)43
b Fv(\012)1264 4464 y Fo(1)1348 4450 y Fv(=)h(\()p Fp(!)1555
4464 y Fo(1)1595 4450 y Fp(;)15 b(!)1692 4464 y Fo(2)1731
4450 y Fp(;)g(:)g(:)g(:)i(;)e(!)1990 4464 y Fn(N)2046
4473 y Fm(1)2084 4450 y Fv(\))44 b Fi(and)g Fv(\012)2416
4464 y Fo(2)2500 4450 y Fv(=)g(\()p Fp(!)2707 4464 y
Fn(N)2763 4473 y Fm(1)2798 4464 y Fo(+1)2892 4450 y Fp(;)15
b(!)2989 4464 y Fn(N)3045 4473 y Fm(1)3080 4464 y Fo(+2)3174
4450 y Fp(;)g(:)g(:)g(:)i(;)e(!)3433 4464 y Fn(N)3489
4473 y Fm(1)3523 4464 y Fo(+)p Fn(N)3634 4473 y Fm(2)3673
4450 y Fv(\))165 4563 y Fi(if)32 b(it)h(c)-5 b(an)33
b(b)-5 b(e)33 b(r)-5 b(epr)g(esente)g(d)34 b(as)g(a)f(F)-7
b(ourier)33 b(series)g(of)g(the)g(typ)-5 b(e)1004 4767
y Fp(f)10 b Fv(\()p Fp(t;)15 b(')p Fv(\))26 b(=)1608
4686 y Fg(X)1383 4881 y Fo(\()p Fn(k)1447 4890 y Fm(1)1482
4881 y Fn(;k)1539 4890 y Fm(2)1573 4881 y Fo(\))p Fx(2)p
Fe(Z)1686 4859 y Ff(N)1734 4874 y Fm(1)1773 4881 y Fx(\002)p
Fe(Z)1867 4859 y Ff(N)1915 4874 y Fm(2)1969 4767 y Fp(f)2014
4782 y Fn(k)2051 4791 y Fm(1)2084 4782 y Fn(k)2121 4791
y Fm(2)2160 4767 y Fp(e)2202 4730 y Fn(i)p Fx(h)p Fn(k)2290
4739 y Fm(1)2325 4730 y Fn(;)p Fo(\012)2396 4739 y Fm(1)2430
4730 y Fx(i)p Fn(t)p Fo(+)p Fn(i)p Fx(h)p Fn(k)2625 4739
y Fm(2)2661 4730 y Fn(;)p Fo(\012)2732 4739 y Fm(2)2766
4730 y Fx(i)p Fn(')2844 4767 y Fp(:)652 b Fv(\(1.5\))165
5069 y Fi(The)31 b(set)h(of)f(al)5 b(l)32 b(quasi-p)-5
b(erio)g(dic)33 b(r)-5 b(e)g(al)33 b(analytic)f(functions)g(with)g(fr)
-5 b(e)g(quencies)31 b Fv(\012)2930 5083 y Fo(1)3001
5069 y Fi(and)h Fv(\012)3242 5083 y Fo(2)3312 5069 y
Fi(is)f(denote)-5 b(d)165 5182 y(by)32 b Fp(Q)p Fv(\(\012)456
5196 y Fo(1)496 5182 y Fp(;)15 b Fv(\012)602 5196 y Fo(2)641
5182 y Fv(\))p Fi(.)1914 5691 y Fv(3)p eop end
%%Page: 4 4
TeXDict begin 4 3 bop 165 337 a Fv(The)30 b(F)-8 b(ourier)31
b(co)s(e\016cien)m(ts)h Fp(f)1172 352 y Fn(k)1209 361
y Fm(1)1243 352 y Fn(k)1280 361 y Fm(2)1348 337 y Fv(in)e(\(1)p
Fp(:)p Fv(5\))j(yield)d(the)h(shell)f(function)1096 568
y Fp(F)13 b Fv(\()p Fp(\022)s(;)1295 541 y Fg(e)1288
568 y Fp(\022)r Fv(\))26 b(=)1715 487 y Fg(X)1490 682
y Fo(\()p Fn(k)1554 691 y Fm(1)1588 682 y Fn(;k)1645
691 y Fm(2)1679 682 y Fo(\))p Fx(2)p Fe(Z)1792 660 y
Ff(N)1840 675 y Fm(1)1879 682 y Fx(\002)p Fe(Z)1973 660
y Ff(N)2021 675 y Fm(2)2075 568 y Fp(f)2120 583 y Fn(k)2157
592 y Fm(1)2191 583 y Fn(k)2228 592 y Fm(2)2266 568 y
Fp(e)2308 531 y Fn(i)p Fx(h)p Fn(k)2396 540 y Fm(1)2432
531 y Fn(;\022)r Fx(i)p Fo(+)p Fn(i)p Fx(h)p Fn(k)2657
540 y Fm(2)2691 531 y Fn(;)2711 521 y Fg(e)2711 531 y
Fn(\022)r Fx(i)3521 568 y Fv(\(1.6\))165 894 y(for)f
Fp(f)34 b Fv(whic)m(h)25 b(is)g(2)p Fp(\031)s Fv(-p)s(erio)s(dic)g(in)g
(eac)m(h)h(comp)s(onen)m(t)f(of)g(the)h(t)m(w)m(o)g(v)m(ectors)h
Fp(\022)g Fv(=)e(\()p Fp(\022)2916 908 y Fo(1)2955 894
y Fp(;)15 b(:)g(:)g(:)i(;)e(;)g(\022)3240 908 y Fn(N)3296
917 y Fm(1)3335 894 y Fv(\))26 b(and)3574 866 y Fg(e)3567
894 y Fp(\022)h Fv(=)165 1007 y(\()207 979 y Fg(e)200
1007 y Fp(\022)243 1021 y Fn(N)299 1030 y Fm(1)333 1021
y Fo(+1)428 1007 y Fp(;)15 b(:)g(:)g(:)h(;)637 979 y
Fg(e)630 1007 y Fp(\022)673 1021 y Fn(N)729 1030 y Fm(1)763
1021 y Fo(+)p Fn(N)874 1030 y Fm(2)913 1007 y Fv(\),)33
b(and)e(satis\014es)h Fp(f)10 b Fv(\()p Fp(t;)15 b(')p
Fv(\))29 b Fq(\021)e Fp(F)13 b Fv(\(\012)2076 1021 y
Fo(1)2116 1007 y Fp(t;)i Fv(\012)2255 1021 y Fo(2)2294
1007 y Fp(')p Fv(\))33 b(iden)m(tically)g(in)f Fp(t)g
Fv(and)f Fp(')p Fv(.)46 b(F)-8 b(rom)32 b(the)165 1120
y(shell)22 b(function)g Fp(F)38 b Fv(:)26 b Fh(T)914
1087 y Fn(N)970 1096 y Fm(1)1012 1120 y Fq(\002)s Fh(T)1141
1087 y Fn(N)1197 1096 y Fm(2)1262 1120 y Fq(\000)-16
b(!)25 b Fh(R)d Fv(\(where)g Fh(T)k Fv(=)f Fh(R)p Fp(=)p
Fv(\(2)p Fp(\031)s Fh(Z)p Fv(\)\))f(the)e(in)m(v)m(erse)h(F)-8
b(ourier)23 b(transformation)860 1362 y Fp(f)905 1377
y Fn(k)942 1386 y Fm(1)976 1377 y Fn(;k)1033 1386 y Fm(2)1096
1362 y Fv(=)1385 1300 y(1)p 1202 1341 412 4 v 1202 1424
a(\(2)p Fp(\031)s Fv(\))1372 1398 y Fn(N)1428 1407 y
Fm(1)1464 1398 y Fo(+)p Fn(N)1575 1407 y Fm(2)1639 1247
y Fg(Z)1685 1436 y Fe(T)1724 1414 y Ff(N)1772 1429 y
Fm(1)1806 1414 y(+)p Ff(N)1901 1429 y Fm(2)1959 1362
y Fp(F)13 b Fv(\()p Fp(\022)s(;)2158 1335 y Fg(e)2151
1362 y Fp(\022)r Fv(\))p Fp(e)2273 1324 y Fx(\000)p Fn(i)p
Fo(\()p Fx(h)p Fn(k)2443 1333 y Fm(1)2479 1324 y Fn(;\022)r
Fx(i)p Fo(+)p Fx(h)p Fn(k)2680 1333 y Fm(2)2715 1324
y Fn(;)2735 1314 y Fg(e)2735 1324 y Fn(\022)q Fx(i)p
Fo(\))2828 1362 y Fp(d\022)s(d)2975 1335 y Fg(e)2968
1362 y Fp(\022)165 1622 y Fv(yields)41 b(bac)m(k)g(the)g(\(F)-8
b(ourier)42 b(co)s(e\016cien)m(ts)h(of)e(the\))g(quasi-p)s(erio)s(dic)f
(function)h Fp(f)52 b Fv(:)43 b Fh(R)3154 1589 y Fo(2)3236
1622 y Fq(\000)-16 b(!)43 b Fh(R)p Fv(.)72 b(W)-8 b(e)165
1735 y(denote)31 b(b)m(y)1239 1869 y Fp(F)1310 1832 y
Fn(K)1378 1869 y Fv(\()p Fp(\022)s(;)1506 1842 y Fg(e)1499
1869 y Fp(\022)r Fv(\))26 b(=)1739 1788 y Fg(X)1701 1977
y Fx(j)p Fn(k)r Fx(j\024)p Fn(K)1913 1869 y Fp(f)1958
1884 y Fn(k)1995 1893 y Fm(1)2029 1884 y Fn(;k)2086 1893
y Fm(2)2124 1869 y Fp(e)2166 1832 y Fn(i)p Fx(h)p Fn(k)2254
1841 y Fm(1)2289 1832 y Fn(;\022)r Fx(i)p Fo(+)p Fn(i)p
Fx(h)p Fn(k)2514 1841 y Fm(2)2548 1832 y Fn(;)2568 1822
y Fg(e)2568 1832 y Fn(\022)r Fx(i)3521 1869 y Fv(\(1.7\))165
2132 y(the)c(truncation)h(of)f(the)g(F)-8 b(ourier)23
b(series)f(\(1)p Fp(:)p Fv(6\))i(of)e Fp(F)36 b Fv(up)21
b(to)h(order)g Fp(K)7 b Fv(.)38 b(Because)23 b(of)f(real)h(analyticit)m
(y)i(the)165 2245 y(shell)34 b(function)f(is)h(b)s(ounded)e(in)h(a)i
(complex)f(neigh)m(b)s(ourho)s(o)s(d)e(of)i Fh(T)2540
2212 y Fn(N)2596 2221 y Fm(1)2631 2212 y Fo(+)p Fn(N)2742
2221 y Fm(2)2814 2245 y Fv(de\014ned)f(b)m(y)h(inequalities)165
2358 y Fq(j)15 b Fv(Im)g Fp(\022)372 2372 y Fn(i)400
2358 y Fq(j)40 b(\024)g Fp(r)s Fv(,)h Fq(j)15 b Fv(Im)858
2330 y Fg(e)851 2358 y Fp(\022)894 2372 y Fn(j)930 2358
y Fq(j)40 b(\024)g Fp(r)i Fv(for)d(some)h Fp(r)i(>)e
Fv(0.)68 b(F)-8 b(or)40 b(\014xed)f Fp(r)k(>)d Fv(0)f(w)m(e)h(denote)g
(b)m(y)f Fp(Q)3238 2372 y Fn(r)3276 2358 y Fv(\(\012)3377
2372 y Fo(1)3416 2358 y Fp(;)15 b Fv(\012)3522 2372 y
Fo(2)3562 2358 y Fv(\))40 b Fq(\032)165 2471 y Fp(Q)p
Fv(\(\012)338 2485 y Fo(1)377 2471 y Fp(;)15 b Fv(\012)483
2485 y Fo(2)523 2471 y Fv(\))24 b(the)f(set)h(of)g(real)g(analytic)i
(functions)d Fp(f)32 b Fv(suc)m(h)24 b(that)g(the)g(corresp)s(onding)e
(shell)i(functions)f Fp(F)165 2584 y Fv(are)30 b(b)s(ounded)d(on)i(the)
h(subset)f(\005)1313 2598 y Fn(r)1376 2584 y Fv(=)c Fq(f)p
Fv(\()p Fp(\022)s(;)1646 2556 y Fg(e)1639 2584 y Fp(\022)r
Fv(\))g Fq(2)g Fh(C)1890 2551 y Fn(N)1946 2560 y Fm(1)2003
2584 y Fq(\002)18 b Fh(C)2152 2551 y Fn(N)2208 2560 y
Fm(2)2272 2584 y Fv(:)26 b Fq(j)15 b Fv(Im)g Fp(\022)2530
2598 y Fn(i)2558 2584 y Fq(j)25 b(\024)g Fp(r)m(;)15
b Fq(j)g Fv(Im)2954 2556 y Fg(e)2947 2584 y Fp(\022)2990
2598 y Fn(j)3026 2584 y Fq(j)26 b(\024)f Fp(r)s Fq(g)p
Fv(.)40 b(Using)30 b(the)165 2696 y(suprem)m(um)f(norm)614
2986 y Fq(j)p Fp(f)10 b Fq(j)719 3000 y Fn(r)782 2986
y Fv(=)96 b(sup)878 3088 y Fo(\()p Fn(\022)r(;)960 3078
y Fg(e)960 3088 y Fn(\022)r Fo(\))p Fx(2)p Fo(\005)1122
3096 y Ff(r)1172 2814 y Fg(\014)1172 2864 y(\014)1172
2913 y(\014)1172 2963 y(\014)1172 3013 y(\014)1172 3063
y(\014)1425 2905 y(X)1200 3100 y Fo(\()p Fn(k)1264 3109
y Fm(1)1299 3100 y Fn(;k)1356 3109 y Fm(2)1390 3100 y
Fo(\))p Fx(2)p Fe(Z)1503 3078 y Ff(N)1551 3093 y Fm(1)1590
3100 y Fx(\002)p Fe(Z)1684 3078 y Ff(N)1732 3093 y Fm(2)1786
2986 y Fp(f)1831 3001 y Fn(k)1868 3010 y Fm(1)1901 3001
y Fn(k)1938 3010 y Fm(2)1977 2986 y Fp(e)2019 2948 y
Fn(i)p Fx(h)p Fn(k)2107 2957 y Fm(1)2142 2948 y Fn(;\022)r
Fx(i)p Fo(+)p Fn(i)p Fx(h)p Fn(k)2367 2957 y Fm(2)2402
2948 y Fn(;)2422 2938 y Fg(e)2422 2948 y Fn(\022)q Fx(i)2488
2814 y Fg(\014)2488 2864 y(\014)2488 2913 y(\014)2488
2963 y(\014)2488 3013 y(\014)2488 3063 y(\014)2541 2986
y Fv(=)g(sup)2637 3088 y Fo(\()p Fn(\022)r(;)2719 3078
y Fg(e)2719 3088 y Fn(\022)q Fo(\))p Fx(2)p Fo(\005)2880
3096 y Ff(r)2931 2889 y Fg(\014)2931 2938 y(\014)2931
2988 y(\014)2958 2986 y Fp(F)13 b Fv(\()p Fp(\022)s(;)3157
2959 y Fg(e)3150 2986 y Fp(\022)s Fv(\))3231 2889 y Fg(\014)3231
2938 y(\014)3231 2988 y(\014)165 3287 y Fv(on)30 b(\005)359
3301 y Fn(r)428 3287 y Fv(and)f(Cauc)m(h)m(y's)i(form)m(ula,)g(it)g
(follo)m(ws)g(that)963 3492 y Fq(j)p Fp(f)1033 3507 y
Fn(k)1070 3516 y Fm(1)1104 3507 y Fn(;k)1161 3516 y Fm(2)1199
3492 y Fq(j)25 b(\024)g(j)p Fp(f)10 b Fq(j)1450 3506
y Fn(r)1488 3492 y Fp(e)1530 3454 y Fx(\000j)p Fn(k)r
Fx(j)p Fn(r)1792 3492 y Fv(and)90 b Fq(j)p Fp(f)2099
3506 y Fn(')2149 3492 y Fq(j)2174 3507 y Fn(r)2208 3488
y Fl(0)2260 3492 y Fq(\024)25 b Fv(\()p Fp(r)e Fq(\000)d
Fp(r)2590 3454 y Fx(0)2613 3492 y Fv(\))2648 3454 y Fx(\000)p
Fo(1)2742 3492 y Fq(j)p Fp(f)10 b Fq(j)2847 3506 y Fn(r)2885
3492 y Fp(:)611 b Fv(\(1.8\))165 3696 y(for)30 b Fp(f)35
b Fq(2)24 b Fp(Q)541 3710 y Fn(r)579 3696 y Fv(\(\012)680
3710 y Fo(1)720 3696 y Fp(;)15 b Fv(\012)826 3710 y Fo(2)865
3696 y Fv(\))31 b(and)f(0)25 b Fp(<)g(r)1318 3663 y Fx(0)1366
3696 y Fp(<)g(r)s Fv(.)40 b(F)-8 b(or)32 b Fp(r)m(;)15
b(s)25 b(>)g Fv(0)31 b(w)m(e)g(de\014ne)477 3900 y Fp(D)552
3914 y Fn(r)n(;s)664 3900 y Fv(=)25 b Fq(f)p Fp(I)33
b Fq(2)25 b Fh(C)g Fv(:)g Fq(j)p Fp(I)7 b Fq(j)26 b Fp(<)f(s)p
Fq(g)20 b(\002)g Fv(\005)1585 3914 y Fn(r)1649 3900 y
Fv(=)25 b Fq(f)p Fv(\()p Fp(I)7 b(;)15 b(\022)s(;)2006
3873 y Fg(e)1999 3900 y Fp(\022)r Fv(\))25 b(:)h Fq(j)p
Fp(I)7 b Fq(j)26 b Fp(<)f(s;)15 b Fq(j)g Fv(Im)g Fp(\022)2664
3914 y Fn(i)2692 3900 y Fq(j)25 b Fp(<)g(r)m(;)15 b Fq(j)g
Fv(Im)3088 3873 y Fg(e)3081 3900 y Fp(\022)3124 3914
y Fn(j)3160 3900 y Fq(j)26 b Fp(<)f(r)s Fq(g)165 4104
y Fv(and)30 b(for)g Fp(\015)g(>)25 b Fv(0)31 b(w)m(e)g(de\014ne)e(the)i
(set)547 4319 y Fp(A)615 4333 y Fn(\015)685 4319 y Fv(=)781
4225 y Fg(n)836 4319 y Fp(a)25 b Fq(2)g Fh(R)g Fv(:)h
Fq(jh)p Fp(k)1238 4333 y Fo(1)1278 4319 y Fp(;)15 b Fv(\012)1384
4333 y Fo(1)1424 4319 y Fq(i)20 b Fv(+)g Fq(h)p Fp(k)1652
4333 y Fo(2)1692 4319 y Fp(;)15 b(a)p Fv(\012)1846 4333
y Fo(2)1886 4319 y Fq(ij)26 b(\025)f Fp(\015)5 b Fv(\010\()p
Fq(j)p Fp(k)s Fq(j)p Fv(\))26 b(for)k(all)h(0)26 b Fq(6)p
Fv(=)f Fp(k)k Fq(2)24 b Fh(Z)3030 4286 y Fn(N)3086 4295
y Fm(2)3121 4286 y Fo(+)p Fn(N)3232 4295 y Fm(2)3271
4225 y Fg(o)165 4539 y Fv(with)30 b(its)h(complex)g(neigh)m(b)s(ourho)s
(o)s(d)d Fp(O)1545 4554 y Fn(h)1616 4539 y Fv(:=)d Fp(A)1805
4553 y Fn(\015)1870 4539 y Fv(+)20 b Fp(h)30 b Fv(of)h(radius)e
Fp(h)i Fv(and)f(put)f Fq(j)21 b(\001)f(j)2962 4554 y
Fn(r)n(;s;h)3134 4539 y Fv(=)91 b(sup)3230 4604 y Ff(D)3280
4612 y(r)n(;s)3359 4604 y Fl(\002)p Ff(O)3454 4622 y(h)3498
4539 y Fq(j)21 b(\001)f(j)p Fv(.)165 4814 y Fj(De\014nition)35
b(1.5)46 b Fi(L)-5 b(et)33 b Fp(f)i Fq(2)24 b Fp(Q)p
Fv(\(\012)1327 4828 y Fo(1)1367 4814 y Fp(;)15 b Fv(\012)1473
4828 y Fo(2)1512 4814 y Fv(\))33 b Fi(have)g(the)g(shel)5
b(l)33 b(function)g Fp(F)13 b Fi(.)42 b(The)33 b(F)-7
b(ourier)33 b(c)-5 b(o)g(e\016cient)1204 5056 y Fp(f)1249
5070 y Fo(00)1348 5056 y Fv(=)1637 4995 y(1)p 1454 5035
V 1454 5119 a(\(2)p Fp(\031)s Fv(\))1624 5092 y Fn(N)1680
5101 y Fm(1)1716 5092 y Fo(+)p Fn(N)1827 5101 y Fm(2)1891
4941 y Fg(Z)1937 5130 y Fe(T)1976 5108 y Ff(N)2024 5123
y Fm(1)2059 5108 y(+)p Ff(N)2154 5123 y Fm(2)2211 5056
y Fp(F)13 b Fv(\()p Fp(\022)s(;)2411 5029 y Fg(e)2403
5056 y Fp(\022)s Fv(\))p Fp(d\022)s(d)2631 5029 y Fg(e)2624
5056 y Fp(\022)165 5309 y Fi(is)32 b(c)-5 b(al)5 b(le)-5
b(d)34 b(the)f(aver)-5 b(age)34 b(of)f Fp(f)41 b Fi(and)34
b(denote)-5 b(d)34 b(by)f Fv(a)m(v)r(\()p Fp(f)10 b Fv(\))p
Fi(.)1914 5691 y Fv(4)p eop end
%%Page: 5 5
TeXDict begin 5 4 bop 165 337 a Fv(F)-8 b(or)43 b(a)f(quasi-p)s(erio)s
(dic)f(function)h Fp(v)j Fv(with)d(rationally)h(indep)s(enden)m(t)e
(frequencies)h Fp(!)3182 351 y Fo(1)3221 337 y Fp(;)15
b(:)g(:)g(:)h(;)f(!)3479 352 y Fn(d)3562 337 y Fv(and)165
450 y(shell)30 b(function)g Fp(V)21 b Fv(,)30 b(satisfying)h
Fp(v)s Fv(\()p Fp(t)p Fv(\))26 b(=)f Fp(V)c Fv(\()p Fp(!)1700
464 y Fo(1)1739 450 y Fp(t;)15 b(:)g(:)g(:)h(;)f(!)2030
465 y Fn(d)2071 450 y Fp(t)p Fv(\),)31 b(the)f(time)h(a)m(v)m(erage)
1623 687 y(lim)1590 746 y Fn(T)10 b Fx(!1)1818 625 y
Fv(1)p 1808 666 66 4 v 1808 749 a Fp(T)1898 572 y Fg(Z)1981
598 y Fn(T)1945 761 y Fo(0)2052 687 y Fp(v)s Fv(\()p
Fp(t)p Fv(\))p Fp(dt)165 904 y Fv(coincides)31 b(with)f(the)h(space)g
(a)m(v)m(erage)1500 1123 y Fp(v)1544 1137 y Fo(0)1609
1123 y Fv(=)1798 1061 y(1)p 1714 1102 212 4 v 1714 1185
a(\(2)p Fp(\031)s Fv(\))1884 1159 y Fn(d)1951 1008 y
Fg(Z)1997 1197 y Fe(T)2036 1178 y Ff(d)2092 1123 y Fp(V)20
b Fv(\()p Fp(\022)s Fv(\))p Fp(d\022)165 1357 y Fv(and)30
b(w)m(e)g(denote)h(the)g(common)g(v)-5 b(alue)30 b(b)m(y)h(a)m(v)r(\()p
Fp(v)s Fv(\))g(as)g(w)m(ell.)165 1640 y Fr(2)135 b(Quasi-p)t(erio)t
(dic)45 b(solutions)165 1843 y Fv(In)28 b(this)h(section,)h(w)m(e)f
(\014rst)f(study)g(the)h(existence)i(of)e(quasi-p)s(erio)s(dic)f
(solutions)h(for)g(a)g(2-dimensional)165 1956 y(rev)m(ersible)k
(system.)47 b(Then)31 b(w)m(e)i(deriv)m(e)g(a)f(similar)h(result)f(in)g
(the)h(Hamiltonian)h(case.)47 b(Our)31 b(pro)s(of)h(is)165
2069 y(based)e(on)g(general)i(ideas)e(of)h(KAM-theory)g(as)g(laid)f
(out)h(in)f([10)q(,)h(11)q(,)f(4)q(,)g(15)q(,)h(16)q(,)f(2)q(].)165
2421 y Fd(2.1)112 b(Rev)m(ersible)38 b(systems)165 2593
y Fv(Consider)29 b(the)i(rev)m(ersible)g(system)1448
2695 y Fg(\()1578 2761 y Fv(_)1557 2784 y Fp(I)h Fv(=)25
b Fp(R)q Fv(\()p Fp(I)7 b(;)15 b(';)g(t;)g(a)p Fv(\))1581
2897 y(_)-49 b Fp(')26 b Fv(=)e Fp(a)d Fv(+)f Fp(Q)p
Fv(\()p Fp(I)7 b(;)15 b(';)g(t;)g(a)p Fv(\))p Fp(;)3521
2839 y Fv(\(2.1\))165 3089 y(with)22 b(a)h(parameter)g
Fp(a)i Fq(2)g Fh(R)p Fv(.)38 b(W)-8 b(e)24 b(assume)e(that)h(for)g
(\014xed)e Fp(I)30 b Fv(and)22 b Fp(a)g Fv(w)m(e)h(ha)m(v)m(e)h
Fp(R)q Fv(\()p Fp(I)7 b(;)15 b Fq(\001)p Fp(;)g Fq(\001)p
Fp(;)g(a)p Fv(\))p Fp(;)g(Q)p Fv(\()p Fp(I)7 b(;)15 b
Fq(\001)p Fp(;)g Fq(\001)p Fp(;)g(a)p Fv(\))31 b Fq(2)165
3202 y Fp(Q)237 3216 y Fn(r)275 3202 y Fv(\(\012)376
3216 y Fo(1)415 3202 y Fp(;)15 b Fv(\012)521 3216 y Fo(2)561
3202 y Fv(\))44 b(and)f(the)g(corresp)s(onding)g(shell)h(functions)2242
3176 y Fg(e)2223 3202 y Fp(R)q Fv(\()p Fp(I)7 b(;)2423
3175 y Fg(e)2415 3202 y Fp(\022)s(;)15 b(\022)s(;)g(a)p
Fv(\))44 b(and)2924 3176 y Fg(e)2904 3202 y Fp(Q)o Fv(\()p
Fp(I)7 b(;)3105 3175 y Fg(e)3098 3202 y Fp(\022)r(;)15
b(\022)s(;)g(a)p Fv(\))44 b(are)g(real)165 3315 y(analytic)32
b(on)e Fp(D)712 3329 y Fn(r)n(;s)819 3315 y Fq(\002)20
b Fp(O)979 3330 y Fn(h)1024 3315 y Fv(,)30 b(satisfying)1367
3500 y Fq(j)1412 3474 y Fg(e)1392 3500 y Fp(R)q Fq(j)1487
3515 y Fn(r)n(;s;h)1659 3500 y Fp(<)25 b(\015)5 b(s)1850
3463 y Fo(2)1889 3500 y Fp(;)107 b Fq(j)2067 3474 y Fg(e)2046
3500 y Fp(Q)p Fq(j)2143 3515 y Fn(r)n(;s;h)2315 3500
y Fp(<)25 b(\015)5 b(s)1015 b Fv(\(2.2\))165 3686 y(and)673
3798 y Fp(R)q Fv(\()p Fp(I)7 b(;)15 b Fq(\000)p Fp(';)g
Fq(\000)p Fp(t;)g(a)p Fv(\))26 b(=)f Fq(\000)p Fp(R)q
Fv(\()p Fp(I)7 b(;)15 b(';)g(t;)g(a)p Fv(\))p Fp(;)108
b(Q)p Fv(\()p Fp(I)7 b(;)15 b Fq(\000)p Fp(';)g Fq(\000)p
Fp(t;)g(a)p Fv(\))27 b(=)e Fp(Q)p Fv(\()p Fp(I)7 b(;)15
b(';)g(t;)g(a)p Fv(\))323 b(\(2.3\))165 3956 y(for)23
b(all)i(\()p Fp(I)7 b(;)15 b(';)g(t;)g(a)p Fv(\))28 b
Fq(2)d(fj)p Fp(I)7 b Fq(j)26 b Fp(<)f(s)p Fq(g)7 b(\002)g
Fh(R)1405 3923 y Fo(2)1452 3956 y Fq(\002)g Fp(O)1599
3971 y Fn(h)1644 3956 y Fv(.)38 b(Subsequen)m(tly)-8
b(,)25 b(w)m(e)f(sa)m(y)h(that)f Fp(R)h Fv(is)f(an)f(o)s(dd)g(function)
h(and)165 4069 y Fp(Q)30 b Fv(is)g(an)h(ev)m(en)g(function)f(if)g
(\(2.3\))i(is)f(iden)m(tically)h(satis\014ed,)f(whence)f(\(2)p
Fp(:)p Fv(1\))i(is)f(a)f(rev)m(ersible)h(system.)165
4262 y Fj(Theorem)k(2.1)46 b Fi(Under)28 b(the)h(ab)-5
b(ove)29 b(assumptions)h(and)g(if)e(the)g(Bruno)h(c)-5
b(ondition)30 b(\(1.4\))f(holds,)i(ther)-5 b(e)165 4375
y(is)40 b(an)g Fp(s)450 4342 y Fx(\003)529 4375 y Fi(such)h(that)g(for)
g(any)f(p)-5 b(ositive)41 b Fp(s)e(<)f(s)1840 4342 y
Fx(\003)1919 4375 y Fi(ther)-5 b(e)41 b(is)f(a)h(function)f
Fp(a)2758 4389 y Fo(0)2836 4375 y Fv(:)f Fp(A)2968 4389
y Fn(\015)3051 4375 y Fq(\000)-15 b(!)39 b Fh(R)g Fi(satisfying)165
4488 y Fq(j)p Fp(a)238 4502 y Fo(0)278 4488 y Fv(\()p
Fp(\013)p Fv(\))21 b Fq(\000)f Fp(\013)p Fq(j)26 b Fp(<)f(h)33
b Fi(for)g(al)5 b(l)33 b Fp(\013)26 b Fq(2)f Fp(A)1321
4502 y Fn(\015)1398 4488 y Fi(and)33 b(a)g(change)g(of)g(variables)911
4673 y Fp(I)f Fv(=)25 b Fp(\045)20 b Fv(+)g Fp(v)s Fv(\()p
Fp(\045;)15 b( )s(;)g(\022)s(;)g(\013)p Fv(\))p Fp(;)111
b(')26 b Fv(=)f Fp( )e Fv(+)d Fp(u)p Fv(\()p Fp( )s(;)15
b(\022)s(;)g(\013)p Fv(\))p Fp(;)110 b(\013)26 b Fq(2)f
Fp(A)2918 4687 y Fn(\015)3521 4673 y Fv(\(2.4\))165 4859
y Fi(which)33 b(tr)-5 b(ansforms)36 b(system)d(\(2.1\))h(with)f
Fp(a)26 b Fv(=)f Fp(a)1816 4873 y Fo(0)1855 4859 y Fv(\()p
Fp(\013)p Fv(\))34 b Fi(into)f(a)g(system)1162 5044 y
Fv(_)-43 b Fp(\045)25 b Fv(=)g Fp(V)20 b Fv(\()p Fp(\045;)15
b( )s(;)g(t;)g(\013)p Fv(\))p Fp(;)1940 5020 y Fv(_)1911
5044 y Fp( )29 b Fv(=)c Fp(\013)c Fv(+)f Fp(U)10 b Fv(\()p
Fp(\045;)15 b( )s(;)g(t;)g(\013)p Fv(\))794 b(\(2.5\))165
5229 y Fi(such)33 b(that)987 5362 y Fp(V)20 b Fv(\(0)p
Fp(;)15 b( )s(;)g(t;)g(\013)p Fv(\))28 b(=)1582 5301
y Fp(@)5 b(V)p 1582 5341 127 4 v 1595 5424 a(@)g(\045)1719
5362 y Fv(\(0)p Fp(;)15 b( )s(;)g(t;)g(\013)p Fv(\))28
b(=)d Fp(U)10 b Fv(\(0)p Fp(;)15 b( )s(;)g(t;)g(\013)p
Fv(\))29 b(=)c(0)p Fp(:)635 b Fv(\(2.6\))1914 5691 y(5)p
eop end
%%Page: 6 6
TeXDict begin 6 5 bop 165 337 a Fv(It)30 b(follo)m(ws)i(that)f(for)f
(eac)m(h)h Fp( )1161 351 y Fo(0)1231 337 y Fv(the)g(system)g(\(2.1\))h
(admits)e(the)h(quasi-p)s(erio)s(dic)f(solution)602 533
y Fp(I)7 b Fv(\()p Fp(t)p Fv(\))26 b(=)f Fp(v)s Fv(\(0)p
Fp(;)15 b( )1100 547 y Fo(0)1161 533 y Fv(+)20 b Fp(\013t;)15
b Fv(\012)1449 547 y Fo(1)1489 533 y Fp(t;)g(\013)p Fv(\))p
Fp(;)108 b(')p Fv(\()p Fp(t)p Fv(\))26 b(=)f Fp( )2131
547 y Fo(0)2191 533 y Fv(+)20 b Fp(\013t)g Fv(+)g Fp(u)p
Fv(\(0)p Fp(;)15 b( )2715 547 y Fo(0)2776 533 y Fv(+)20
b Fp(\013t;)15 b Fv(\012)3064 547 y Fo(1)3104 533 y Fp(t;)g(\013)p
Fv(\))165 729 y(with)30 b(frequency)g(v)m(ectors)i(\012)1159
743 y Fo(1)1228 729 y Fv(and)e Fp(\013)p Fv(\012)1529
743 y Fo(2)1568 729 y Fv(.)165 941 y Fi(Pr)-5 b(o)g(of.)42
b Fv(An)27 b(essen)m(tial)h(idea)g(of)f(the)g(KAM)g(metho)s(d)f(is)h
(to)h(construct)f(a)h(simplifying)f(transformation,)165
1054 y(consisting)42 b(of)f(in\014nitely)g(man)m(y)g(successiv)m(e)h
(steps)f(\(referred)g(to)h(as)f(KAM)g(steps\))g(of)g(iterations,)165
1167 y(so)35 b(that)g(after)g(eac)m(h)h(step)e(the)h(new)f(p)s
(erturbation)g(terms)g(of)h(the)g(transformed)e(system)i(are)g(m)m(uc)m
(h)165 1279 y(smaller)44 b(than)g(the)g(ones)g(in)g(the)g(previous)f
(system.)82 b(As)44 b(all)g(KAM)g(steps)g(can)g(b)s(e)g(carried)g(out)
165 1392 y(inductiv)m(ely)-8 b(,)32 b(b)s(elo)m(w,)f(w)m(e)f(only)h
(describ)s(e)f(one)g(step)h(of)f(KAM)h(iteration)h(in)e(more)g(detail.)
306 1505 y(Let)37 b(\010)f(b)s(e)f(an)h(appro)m(ximation)i(function)e
(as)g(de\014ned)f(in)h(De\014nition)h(1.2.)60 b(W)-8
b(e)37 b(c)m(ho)s(ose)g Fp(\034)46 b(>)34 b Fv(0,)165
1618 y(0)26 b Fp(<)f(\026)g(<)g Fv(1)p Fp(=)p Fv(4,)31
b Fp($)d Fq(\025)d Fp(N)971 1632 y Fo(1)1031 1618 y Fv(+)20
b Fp(N)1195 1632 y Fo(2)1255 1618 y Fv(+)g(2)30 b(and)g
Fp(T)1651 1632 y Fo(0)1721 1618 y Fv(su\016cien)m(tly)h(large)h(suc)m
(h)e(that)555 1890 y(\010\()p Fp(T)709 1904 y Fo(0)749
1890 y Fv(\))25 b Fp(<)g(e)947 1852 y Fn($)1012 1890
y Fp(\026)1067 1852 y Fn(\034)1201 1890 y Fv(and)1454
1775 y Fg(Z)1537 1801 y Fx(1)1500 1964 y Fn(T)1541 1973
y Fm(0)1627 1890 y Fv(log)1857 1828 y(1)p 1769 1869 221
4 v 1769 1952 a(\010\()p Fp(K)7 b Fv(\))2009 1828 y Fp(dK)p
2009 1869 132 4 v 2013 1952 a(K)2097 1926 y Fo(2)2176
1890 y Fp(<)2281 1828 y(r)2322 1842 y Fo(0)p 2281 1869
81 4 v 2299 1952 a Fv(4)2702 1811 y Fp(\034)25 b Fv(log)2913
1775 y Fo(1)p 2910 1790 43 4 v 2910 1843 a Fn(\026)p
2382 1869 901 4 v 2382 1973 a Fv(\()p Fp(N)2490 1987
y Fo(1)2550 1973 y Fv(+)20 b Fp(N)2714 1987 y Fo(2)2753
1973 y Fv(\))15 b(log)2946 1929 y Fo(4\()p Fn(N)3064
1938 y Fm(1)3100 1929 y Fo(+)p Fn(N)3211 1938 y Fm(2)3245
1929 y Fo(\))p 2946 1952 327 4 v 3088 2004 a Fn(\026)3292
1890 y Fp(:)165 2177 y Fv(F)-8 b(ollo)m(wing)33 b([16)q(],)e(w)m(e)f
(de\014ne)g(the)h(function)1384 2374 y(\011\()p Fp(T)13
b Fv(\))26 b(:=)f Fp(T)1804 2336 y Fx(\000)p Fn($)1923
2374 y Fv(\010\()p Fp(T)13 b Fv(\))p Fp(;)106 b(T)39
b Fq(\025)24 b Fv(1)165 2570 y(and)30 b(put)1130 2683
y Fp(T)1183 2697 y Fn(\027)1251 2683 y Fv(:=)25 b(\011)1443
2645 y Fx(\000)p Fo(1)1537 2683 y Fv(\(\011\()p Fp(T)1731
2697 y Fo(0)1771 2683 y Fv(\))p Fp(\026)1861 2645 y Fn(\034)8
b(\027)1944 2683 y Fv(\))p Fp(;)106 b(\027)31 b Fq(\025)25
b Fv(0)p Fp(;)107 b(T)2512 2697 y Fo(0)2577 2683 y Fq(\025)25
b Fv(1)p Fp(:)165 2846 y Fv(Clearly)-8 b(,)40 b(w)m(e)e(ha)m(v)m(e)h
(\011)e Fq(&)g Fv(0)h(as)g Fp(T)50 b Fq(!)37 b(1)h Fv(and)f(1)g
Fq(\024)g Fp(T)2090 2860 y Fo(0)2167 2846 y Fp(<)g(T)2328
2860 y Fn(i)2393 2846 y Fp(<)g(T)2554 2860 y Fn(j)2628
2846 y Fv(for)h(0)f Fp(<)g(i)h(<)f(j)43 b Fv(and)37 b(\014xed)g
Fp(\034)10 b Fv(.)165 2959 y(Initially)-8 b(,)37 b(w)m(e)d(set)h(0)d
Fp(<)f(\026)h(<)f(\026)1237 2926 y Fx(\003)1276 2959
y Fv(\()p Fp(<)1424 2923 y Fo(1)p 1424 2938 36 4 v 1424
2990 a(4)1469 2959 y Fv(\))j(for)g Fp(\026)1736 2926
y Fx(\003)1810 2959 y Fv(su\016cien)m(tly)h(small,)g(and)f
Fp(\024)e(>)f(\034)10 b Fv(,)35 b Fp(R)3082 2973 y Fo(0)3153
2959 y Fv(=)d Fp(R)q(;)15 b(Q)3438 2973 y Fo(0)3509 2959
y Fv(=)31 b Fp(Q)p Fv(,)165 3072 y Fp(I)205 3086 y Fo(0)270
3072 y Fv(=)24 b Fp(I)7 b(;)15 b(')511 3086 y Fo(0)577
3072 y Fv(=)25 b Fp(')p Fv(,)31 b Fp(h)840 3086 y Fo(0)905
3072 y Fv(=)25 b Fp(h;)15 b(r)1134 3086 y Fo(0)1200 3072
y Fv(=)25 b Fp(r)i(>)e Fv(0)p Fp(;)15 b Fv(0)27 b Fp(<)e(s)1756
3086 y Fo(0)1820 3072 y Fv(=)g Fp(s)g(<)g Fv(1.)41 b(De\014ne)31
b(the)f(sequences)244 3197 y Fg(8)244 3271 y(>)244 3296
y(>)244 3321 y(>)244 3346 y(>)244 3371 y(>)244 3396 y(>)244
3421 y(<)244 3570 y(>)244 3595 y(>)244 3620 y(>)244 3645
y(>)244 3670 y(>)244 3695 y(>)244 3720 y(:)359 3327 y
Fp(r)400 3341 y Fn(\027)t Fo(+1)558 3327 y Fv(=)25 b
Fp(r)695 3341 y Fn(\027)759 3327 y Fq(\000)860 3283 y
Fo(2\()p Fn(N)978 3292 y Fm(1)1013 3283 y Fo(+)p Fn(N)1124
3292 y Fm(2)1159 3283 y Fo(\))p 860 3306 327 4 v 983
3358 a Fn(T)1024 3366 y Ff(\027)1211 3327 y Fv(log)1354
3283 y Fo(4\()p Fn(N)1472 3292 y Fm(1)1507 3283 y Fo(+)p
Fn(N)1618 3292 y Fm(2)1652 3283 y Fo(\))p 1354 3306 V
1496 3358 a Fn(\026)1690 3327 y Fp(;)106 b(r)1862 3341
y Fn(\027)1931 3327 y Fv(=)25 b Fp(r)2068 3341 y Fo(0)2127
3327 y Fq(\000)20 b Fv(2\()p Fp(N)2371 3341 y Fo(1)2432
3327 y Fv(+)g Fp(N)2596 3341 y Fo(2)2635 3327 y Fv(\))15
b(log)2828 3283 y Fo(4\()p Fn(N)2946 3292 y Fm(1)2981
3283 y Fo(+)p Fn(N)3092 3292 y Fm(2)3127 3283 y Fo(\))p
2828 3306 V 2970 3358 a Fn(\026)3166 3221 y Ff(\027)s
Fl(\000)p Fm(1)3164 3246 y Fg(X)3165 3416 y Ff(\026)p
Fm(=0)3318 3291 y Fo(1)p 3294 3306 83 4 v 3294 3358 a
Fn(T)3335 3366 y Ff(\026)3387 3327 y Fp(;)359 3544 y(s)402
3558 y Fn(\027)470 3544 y Fv(=)25 b Fp(s)609 3558 y Fo(0)648
3544 y Fp(\026)703 3511 y Fn(\024\027)787 3544 y Fp(;)359
3770 y(h)411 3784 y Fn(\027)480 3770 y Fv(=)642 3729
y Fn(\015)p 586 3749 154 4 v 586 3801 a Fo(2)621 3783
y Ff(\027)659 3801 y Fn(T)700 3809 y Ff(\027)749 3770
y Fv(\010\()p Fp(T)903 3784 y Fn(\027)946 3770 y Fv(\))p
Fp(;)3521 3518 y Fv(\(2.7\))165 3970 y(whence)30 b(Lemma)h(13.2)g(in)g
([16)q(])f(implies)h(that)962 4121 y Fx(1)938 4146 y
Fg(X)933 4327 y Fn(\027)t Fo(=0)1113 4165 y Fv(1)p 1087
4206 97 4 v 1087 4289 a Fp(T)1140 4303 y Fn(\027)1219
4227 y Fq(\024)1758 4165 y Fp(r)1799 4179 y Fo(0)p 1325
4206 947 4 v 1325 4310 a Fv(4\()p Fp(N)1478 4324 y Fo(1)1538
4310 y Fv(+)20 b Fp(N)1702 4324 y Fo(2)1742 4310 y Fv(\))15
b(log)1935 4266 y Fo(4\()p Fn(N)2053 4275 y Fm(1)2088
4266 y Fo(+)p Fn(N)2199 4275 y Fm(2)2233 4266 y Fo(\))p
1935 4289 327 4 v 2077 4341 a Fn(\026)2372 4227 y Fv(and)90
b Fp(r)2650 4241 y Fn(\027)2719 4227 y Fq(\025)2824 4165
y Fp(r)2865 4179 y Fo(0)p 2824 4206 81 4 v 2842 4289
a Fv(2)2915 4227 y Fp(:)581 b Fv(\(2.8\))165 4509 y(W)-8
b(e)31 b(supp)s(ose)e(that)i(after)g Fp(\027)36 b Fv(steps,)31
b(the)f(transformed)g(system)g(is)h(of)f(the)h(form)1319
4619 y Fg(8)1319 4693 y(>)1319 4718 y(<)1319 4868 y(>)1319
4893 y(:)1463 4682 y Fv(_)1434 4705 y Fp(I)1474 4719
y Fn(\027)1543 4705 y Fv(=)25 b Fp(R)1708 4719 y Fn(\027)1751
4705 y Fv(\()p Fp(I)1826 4719 y Fn(\027)1869 4705 y Fp(;)15
b(')1968 4719 y Fn(\027)2012 4705 y Fp(;)g(t;)g(a)2173
4719 y Fn(\027)2217 4705 y Fv(\))p Fp(;)1473 4931 y Fv(_)-64
b Fp(')1493 4945 y Fn(\027)1562 4931 y Fv(=)25 b Fp(a)1706
4945 y Fn(\027)1770 4931 y Fv(+)19 b Fp(Q)1932 4945 y
Fn(\027)1976 4931 y Fv(\()p Fp(I)2051 4945 y Fn(\027)2094
4931 y Fp(;)c(')2193 4945 y Fn(\027)2237 4931 y Fp(;)g(t;)g(a)2398
4945 y Fn(\027)2442 4931 y Fv(\))p Fp(;)3478 4816 y Fv(\(2)p
Fp(:)p Fv(9\))3663 4830 y Fn(\027)165 5122 y Fv(where)40
b(the)h(o)s(dd)e(function)i Fp(R)1230 5136 y Fn(\027)1313
5122 y Fv(and)f(the)h(ev)m(en)h(function)e Fp(Q)2323
5136 y Fn(\027)2406 5122 y Fv(are)h(real)h(analytic)g(on)e(the)h
(domain)165 5235 y Fp(D)240 5249 y Fn(r)272 5257 y Ff(\027)310
5249 y Fn(;s)363 5257 y Ff(\027)426 5235 y Fq(\002)19
b Fp(O)585 5249 y Fn(s)618 5257 y Ff(\027)691 5235 y
Fv(and)30 b(ha)m(v)m(e)i(shell)e(functions)g(satisfying)1171
5442 y Fq(j)1211 5416 y Fg(f)1196 5442 y Fp(R)1265 5456
y Fn(\027)1308 5442 y Fq(j)1333 5457 y Fn(r)1365 5465
y Ff(\027)1404 5457 y Fn(;s)1457 5465 y Ff(\027)1495
5457 y Fn(;h)1556 5465 y Ff(\027)1623 5442 y Fp(<)25
b(\015)5 b(s)1814 5405 y Fo(2)1814 5465 y Fn(\027)1857
5442 y Fp(;)106 b Fq(j)2029 5416 y Fg(f)2013 5442 y Fp(Q)2085
5456 y Fn(\027)2128 5442 y Fq(j)2153 5457 y Fn(r)2185
5465 y Ff(\027)2224 5457 y Fn(;s)2277 5465 y Ff(\027)2315
5457 y Fn(;h)2376 5465 y Ff(\027)2443 5442 y Fp(<)25
b(\015)5 b(s)2634 5456 y Fn(\027)2677 5442 y Fp(:)731
b Fv(\(2)p Fp(:)p Fv(10\))3663 5456 y Fn(\027)1914 5691
y Fv(6)p eop end
%%Page: 7 7
TeXDict begin 7 6 bop 165 337 a Fv(W)-8 b(e)30 b(lo)s(ok)f(for)f(a)h(c)
m(hange)g(of)g(v)-5 b(ariables)29 b Fp(S)1557 351 y Fn(\027)1629
337 y Fv(de\014ned)e(in)h(a)h(smaller)g(domain)f Fp(D)2826
351 y Fn(r)2858 360 y Ff(\027)s Fm(+1)2974 351 y Fn(;s)3027
360 y Ff(\027)s Fm(+1)3162 337 y Fq(\002)17 b Fp(O)3319
352 y Fn(h)3360 361 y Ff(\027)s Fm(+1)3479 337 y Fv(,)29
b(suc)m(h)165 450 y(that)34 b(the)g(system)g(\(2)p Fp(:)p
Fv(9\))1015 464 y Fn(\027)1094 450 y Fv(is)g(transformed)f(in)m(to)i
(the)f(form)f(\(2)p Fp(:)p Fv(9\))2452 464 y Fn(\027)t
Fo(+1)2621 450 y Fv(and)h(satis\014es)g(\(2)p Fp(:)p
Fv(10\))3370 464 y Fn(\027)t Fo(+1)3506 450 y Fv(.)51
b(W)-8 b(e)165 562 y(construct)31 b(the)f(desired)g(c)m(hange)i(of)e(v)
-5 b(ariables)31 b Fp(S)1867 576 y Fn(\027)1940 562 y
Fv(in)f(the)h(form)772 688 y Fg(8)772 763 y(>)772 788
y(>)772 813 y(>)772 837 y(>)772 862 y(>)772 887 y(<)772
1037 y(>)772 1062 y(>)772 1087 y(>)772 1111 y(>)772 1136
y(>)772 1161 y(:)888 759 y Fp(I)928 773 y Fn(\027)996
759 y Fv(=)25 b Fp(I)1132 773 y Fn(\027)t Fo(+1)1286
759 y Fv(+)19 b Fp(f)1421 773 y Fn(\027)t Fo(0)1499 759
y Fv(\()p Fp(')1593 773 y Fn(\027)t Fo(+1)1728 759 y
Fp(;)c(t;)g(a)1889 773 y Fn(\027)t Fo(+1)2023 759 y Fv(\))20
b(+)g Fp(f)2214 773 y Fn(\027)t Fo(1)2292 759 y Fv(\()p
Fp(')2386 773 y Fn(\027)t Fo(+1)2520 759 y Fp(;)15 b(t;)g(a)2681
773 y Fn(\027)t Fo(+1)2815 759 y Fv(\))p Fp(I)2890 773
y Fn(\027)t Fo(+1)3024 759 y Fp(;)888 985 y(')947 999
y Fn(\027)1016 985 y Fv(=)25 b Fp(')1171 999 y Fn(\027)t
Fo(+1)1325 985 y Fv(+)19 b Fp(g)1458 999 y Fn(\027)t
Fo(0)1537 985 y Fv(\()p Fp(')1631 999 y Fn(\027)t Fo(+1)1765
985 y Fp(;)c(t;)g(a)1926 999 y Fn(\027)t Fo(+1)2060 985
y Fv(\))p Fp(;)888 1210 y(a)936 1224 y Fn(\027)1004 1210
y Fv(=)25 b Fp(a)1148 1224 y Fn(\027)t Fo(+1)1302 1210
y Fv(+)20 b Fp(\036)1447 1224 y Fn(\027)1490 1210 y Fv(\()p
Fp(a)1573 1224 y Fn(\027)t Fo(+1)1707 1210 y Fv(\))p
Fp(;)3476 985 y Fv(\(2.11\))165 1407 y(where)609 1611
y Fp(f)654 1625 y Fn(\027)t(j)729 1611 y Fv(\()p Fp(')823
1625 y Fn(\027)t Fo(+1)957 1611 y Fp(;)15 b(t;)g(a)1118
1625 y Fn(\027)t Fo(+1)1252 1611 y Fv(\))84 b(=)1609
1530 y Fg(X)1525 1719 y Fx(j)p Fn(k)r Fx(j\024)p Fn(T)1700
1728 y Ff(\027)s Fm(+1)1829 1611 y Fp(f)1884 1567 y Fn(j)1874
1639 y(k)1911 1648 y Fm(1)1945 1639 y Fn(;k)2002 1648
y Fm(2)2040 1611 y Fp(e)2082 1574 y Fn(i)p Fx(h)p Fn(k)2170
1583 y Fm(1)2205 1574 y Fn(;)p Fo(\012)2276 1583 y Fm(1)2310
1574 y Fx(i)p Fn(t)p Fo(+)p Fn(i)p Fx(h)p Fn(k)2505 1583
y Fm(2)2541 1574 y Fn(;)p Fo(\012)2612 1583 y Fm(2)2646
1574 y Fx(i)p Fn(')2719 1583 y Ff(\027)s Fm(+1)2839 1611
y Fp(;)106 b(j)31 b Fv(=)25 b(0)p Fp(;)15 b Fv(1)212
b(\(2.12\))607 1866 y Fp(g)650 1880 y Fn(\027)t Fo(0)729
1866 y Fv(\()p Fp(')823 1880 y Fn(\027)t Fo(+1)957 1866
y Fp(;)15 b(t;)g(a)1118 1880 y Fn(\027)t Fo(+1)1252 1866
y Fv(\))84 b(=)1609 1785 y Fg(X)1525 1973 y Fx(j)p Fn(k)r
Fx(j\024)p Fn(T)1700 1982 y Ff(\027)s Fm(+1)1829 1866
y Fp(g)1875 1828 y Fo(0)1872 1888 y Fn(k)1909 1897 y
Fm(1)1944 1888 y Fn(;k)2001 1897 y Fm(2)2039 1866 y Fp(e)2081
1828 y Fn(i)p Fx(h)p Fn(k)2169 1837 y Fm(1)2204 1828
y Fn(;)p Fo(\012)2275 1837 y Fm(1)2309 1828 y Fx(i)p
Fn(t)p Fo(+)p Fn(i)p Fx(h)p Fn(k)2504 1837 y Fm(2)2540
1828 y Fn(;)p Fo(\012)2611 1837 y Fm(2)2645 1828 y Fx(i)p
Fn(')2718 1837 y Ff(\027)s Fm(+1)2838 1866 y Fp(:)613
b Fv(\(2.13\))165 2161 y(In)29 b(the)i(actual)h(construction)f(w)m(e)g
(searc)m(h)g(for)f(the)g(in)m(v)m(erse)i(id)20 b Fq(\000)f
Fp(\033)2474 2175 y Fn(\027)2548 2161 y Fv(of)30 b(id)20
b(+)g Fp(\036)2892 2175 y Fn(\027)2936 2161 y Fv(,)30
b(w)m(orking)h(with)1543 2365 y Fp(a)1591 2379 y Fn(\027)1659
2365 y Fv(=)25 b Fp(a)1803 2379 y Fn(\027)t Fo(+1)1957
2365 y Fv(+)20 b Fp(\033)2100 2379 y Fn(\027)2143 2365
y Fv(\()p Fp(a)2226 2379 y Fn(\027)2270 2365 y Fv(\))p
Fp(:)165 2569 y Fv(It)30 b(follo)m(ws)i(from)e(\(2)p
Fp(:)p Fv(9\))962 2583 y Fn(\027)1007 2569 y Fv(,)g(\(2)p
Fp(:)p Fv(9\))1247 2583 y Fn(\027)t Fo(+1)1413 2569 y
Fv(and)g(\(2.11\))i(that)289 2774 y Fp(R)358 2788 y Fn(\027)401
2774 y Fv(\()p Fp(I)476 2788 y Fn(\027)t Fo(+1)630 2774
y Fv(+)20 b Fp(f)766 2788 y Fn(\027)t Fo(0)864 2774 y
Fv(+)g Fp(f)1000 2788 y Fn(\027)t Fo(1)1078 2774 y Fp(I)1118
2788 y Fn(\027)t Fo(+1)1251 2774 y Fp(;)15 b(')1350 2788
y Fn(\027)t Fo(+1)1504 2774 y Fv(+)20 b Fp(g)1638 2788
y Fn(\027)t Fo(0)1717 2774 y Fp(;)15 b(t;)g(a)1878 2788
y Fn(\027)t Fo(+1)2032 2774 y Fv(+)20 b Fp(\033)2175
2788 y Fn(\027)2218 2774 y Fv(\))614 2954 y(=)83 b Fp(R)837
2968 y Fn(\027)t Fo(+1)990 2954 y Fv(+)1126 2893 y Fp(@)5
b(f)1224 2907 y Fn(\027)t Fo(0)p 1091 2933 247 4 v 1091
3017 a Fp(@)g(')1203 3031 y Fn(\027)t Fo(+1)1347 2954
y Fv(\()p Fp(a)1430 2968 y Fn(\027)t Fo(+1)1584 2954
y Fv(+)20 b Fp(Q)1747 2968 y Fn(\027)t Fo(+1)1880 2954
y Fv(\))h(+)2037 2893 y Fp(@)5 b(f)2135 2907 y Fn(\027)t
Fo(0)p 2037 2933 177 4 v 2082 3017 a Fp(@)g(t)2243 2954
y Fv(+)2379 2893 y Fp(@)g(f)2477 2907 y Fn(\027)t Fo(1)p
2344 2933 247 4 v 2344 3017 a Fp(@)g(')2456 3031 y Fn(\027)t
Fo(+1)2600 2954 y Fv(\()p Fp(a)2683 2968 y Fn(\027)t
Fo(+1)2837 2954 y Fv(+)20 b Fp(Q)3000 2968 y Fn(\027)t
Fo(+1)3133 2954 y Fv(\))p Fp(I)3208 2968 y Fn(\027)t
Fo(+1)727 3195 y Fv(+)828 3133 y Fp(@)5 b(f)926 3147
y Fn(\027)t Fo(1)p 828 3174 177 4 v 873 3257 a Fp(@)g(t)1014
3195 y(I)1054 3209 y Fn(\027)t Fo(+1)1208 3195 y Fv(+)20
b Fp(f)1344 3209 y Fn(\027)t Fo(1)1422 3195 y Fp(R)1491
3209 y Fn(\027)t Fo(+1)3476 3195 y Fv(\(2.14\))165 3420
y(and)491 3624 y Fp(Q)563 3638 y Fn(\027)606 3624 y Fv(\()p
Fp(I)681 3638 y Fn(\027)t Fo(+1)835 3624 y Fv(+)g Fp(f)971
3638 y Fn(\027)t Fo(0)1069 3624 y Fv(+)g Fp(f)1205 3638
y Fn(\027)t Fo(1)1283 3624 y Fp(I)1323 3638 y Fn(\027)t
Fo(+1)1457 3624 y Fp(;)15 b(')1556 3638 y Fn(\027)t Fo(+1)1710
3624 y Fv(+)20 b Fp(g)1844 3638 y Fn(\027)t Fo(0)1923
3624 y Fp(;)15 b(t;)g(a)2084 3638 y Fn(\027)t Fo(+1)2238
3624 y Fv(+)20 b Fp(\033)2381 3638 y Fn(\027)2424 3624
y Fv(\))h(+)e Fp(a)2618 3638 y Fn(\027)t Fo(+1)2772 3624
y Fv(+)h Fp(\033)2915 3638 y Fn(\027)1014 3805 y Fv(=)82
b Fp(a)1215 3819 y Fn(\027)t Fo(+1)1369 3805 y Fv(+)20
b Fp(Q)1532 3819 y Fn(\027)t Fo(+1)1685 3805 y Fv(+)1786
3743 y Fp(@)5 b(g)1882 3757 y Fn(\027)t Fo(0)p 1786 3784
176 4 v 1831 3867 a Fp(@)g(t)1992 3805 y Fv(+)2128 3743
y Fp(@)g(g)2224 3757 y Fn(\027)t Fo(0)p 2092 3784 247
4 v 2092 3867 a Fp(@)g(')2204 3881 y Fn(\027)t Fo(+1)2349
3805 y Fv(\()p Fp(a)2432 3819 y Fn(\027)t Fo(+1)2586
3805 y Fv(+)19 b Fp(Q)2748 3819 y Fn(\027)t Fo(+1)2882
3805 y Fv(\))p Fp(:)534 b Fv(\(2.15\))165 4051 y(Using)30
b(a)h(T)-8 b(a)m(ylor)32 b(expansion,)e(w)m(e)h(ha)m(v)m(e)776
4255 y Fp(R)845 4269 y Fn(\027)888 4255 y Fv(\()p Fp(I)963
4269 y Fn(\027)1007 4255 y Fp(;)15 b(')1106 4269 y Fn(\027)1150
4255 y Fp(;)g(t;)g(a)1311 4269 y Fn(\027)1355 4255 y
Fv(\))25 b(=)g Fp(R)1580 4269 y Fn(\027)t Fo(0)1659 4255
y Fv(\()p Fp(')1753 4269 y Fn(\027)1797 4255 y Fp(;)15
b(t;)g(a)1958 4269 y Fn(\027)2002 4255 y Fv(\))20 b(+)g
Fp(R)2217 4269 y Fn(\027)t Fo(1)2295 4255 y Fv(\()p Fp(')2389
4269 y Fn(\027)2433 4255 y Fp(;)15 b(t;)g(a)2594 4269
y Fn(\027)2638 4255 y Fv(\))p Fp(I)2713 4269 y Fn(\027)2777
4255 y Fv(+)20 b Fp(O)s Fv(\()p Fp(I)3022 4217 y Fo(2)3015
4277 y Fn(\027)3062 4255 y Fv(\))165 4459 y(and)1122
4572 y Fp(Q)1194 4586 y Fn(\027)1237 4572 y Fv(\()p Fp(I)1312
4586 y Fn(\027)1356 4572 y Fp(;)15 b(')1455 4586 y Fn(\027)1499
4572 y Fp(;)g(t;)g(a)1660 4586 y Fn(\027)1704 4572 y
Fv(\))25 b(=)g Fp(Q)1932 4586 y Fn(\027)t Fo(0)2011 4572
y Fv(\()p Fp(')2105 4586 y Fn(\027)2149 4572 y Fp(;)15
b(t;)g(a)2310 4586 y Fn(\027)2353 4572 y Fv(\))21 b(+)f
Fp(O)s Fv(\()p Fp(I)2647 4586 y Fn(\027)2690 4572 y Fv(\))p
Fp(:)165 4739 y Fv(F)-8 b(or)31 b Fp(R)397 4753 y Fn(\027)t
Fo(0)475 4739 y Fp(;)15 b(R)584 4753 y Fn(\027)t Fo(1)694
4739 y Fv(and)29 b Fp(Q)942 4753 y Fn(\027)t Fo(0)1051
4739 y Fv(w)m(e)i(ha)m(v)m(e)585 4943 y Fp(R)654 4957
y Fn(\027)t(j)729 4943 y Fv(\()p Fp(')823 4957 y Fn(\027)867
4943 y Fp(;)15 b(t;)g(a)1028 4957 y Fn(\027)1072 4943
y Fv(\))83 b(=)1569 4862 y Fg(X)1344 5057 y Fo(\()p Fn(k)1408
5066 y Fm(1)1443 5057 y Fn(;k)1500 5066 y Fm(2)1534 5057
y Fo(\))p Fx(2)p Fe(Z)1647 5035 y Ff(N)1695 5050 y Fm(1)1734
5057 y Fx(\002)p Fe(Z)1828 5035 y Ff(N)1876 5050 y Fm(2)1930
4943 y Fp(R)2000 4899 y Fn(j)1999 4971 y(k)2036 4980
y Fm(1)2070 4971 y Fn(k)2107 4980 y Fm(2)2146 4943 y
Fp(e)2188 4905 y Fn(i)p Fx(h)p Fn(k)2276 4914 y Fm(1)2311
4905 y Fn(;)p Fo(\012)2382 4914 y Fm(1)2416 4905 y Fx(i)p
Fn(t)p Fo(+)p Fn(i)p Fx(h)p Fn(k)2611 4914 y Fm(2)2646
4905 y Fn(;)p Fo(\012)2717 4914 y Fm(2)2752 4905 y Fx(i)p
Fn(')2825 4913 y Ff(\027)2868 4943 y Fp(;)106 b(j)31
b Fv(=)25 b(0)p Fp(;)15 b Fv(1)579 5204 y Fp(Q)651 5218
y Fn(\027)t Fo(0)729 5204 y Fv(\()p Fp(')823 5218 y Fn(\027)867
5204 y Fp(;)g(t;)g(a)1028 5218 y Fn(\027)1072 5204 y
Fv(\))83 b(=)1569 5123 y Fg(X)1344 5318 y Fo(\()p Fn(k)1408
5327 y Fm(1)1443 5318 y Fn(;k)1500 5327 y Fm(2)1534 5318
y Fo(\))p Fx(2)p Fe(Z)1647 5295 y Ff(N)1695 5310 y Fm(1)1734
5318 y Fx(\002)p Fe(Z)1828 5295 y Ff(N)1876 5310 y Fm(2)1930
5204 y Fp(Q)2002 5166 y Fo(0)2002 5226 y Fn(k)2039 5235
y Fm(1)2073 5226 y Fn(k)2110 5235 y Fm(2)2148 5204 y
Fp(e)2190 5166 y Fn(i)p Fx(h)p Fn(k)2278 5175 y Fm(1)2314
5166 y Fn(;)p Fo(\012)2385 5175 y Fm(1)2419 5166 y Fx(i)p
Fn(t)p Fo(+)p Fn(i)p Fx(h)p Fn(k)2614 5175 y Fm(2)2649
5166 y Fn(;)p Fo(\012)2720 5175 y Fm(2)2754 5166 y Fx(i)p
Fn(')2827 5174 y Ff(\027)1914 5691 y Fv(7)p eop end
%%Page: 8 8
TeXDict begin 8 7 bop 165 337 a Fv(and)30 b(de\014ne)f(the)i(F)-8
b(ourier)31 b(truncations)680 537 y Fp(R)750 490 y Fn(T)791
499 y Ff(\027)s Fm(+1)749 563 y Fn(\027)t(j)911 537 y
Fv(\()p Fp(')1005 551 y Fn(\027)1049 537 y Fp(;)15 b(t;)g(a)1210
551 y Fn(\027)1254 537 y Fv(\))83 b(=)1611 456 y Fg(X)1526
644 y Fx(j)p Fn(k)r Fx(j\024)p Fn(T)1701 653 y Ff(\027)s
Fm(+1)1830 537 y Fp(R)1900 493 y Fn(j)1899 565 y(k)1936
574 y Fm(1)1971 565 y Fn(k)2008 574 y Fm(2)2046 537 y
Fp(e)2088 500 y Fn(i)p Fx(h)p Fn(k)2176 509 y Fm(1)2211
500 y Fn(;)p Fo(\012)2282 509 y Fm(1)2316 500 y Fx(i)p
Fn(t)p Fo(+)p Fn(i)p Fx(h)p Fn(k)2511 509 y Fm(2)2547
500 y Fn(;)p Fo(\012)2618 509 y Fm(2)2652 500 y Fx(i)p
Fn(')2725 508 y Ff(\027)2768 537 y Fp(;)107 b(j)30 b
Fv(=)25 b(0)p Fp(;)15 b Fv(1)678 795 y Fp(Q)750 748 y
Fn(T)791 757 y Ff(\027)s Fm(+1)750 820 y Fn(\027)t Fo(0)911
795 y Fv(\()p Fp(')1005 809 y Fn(\027)1049 795 y Fp(;)g(t;)g(a)1210
809 y Fn(\027)1254 795 y Fv(\))83 b(=)1611 715 y Fg(X)1526
903 y Fx(j)p Fn(k)r Fx(j\024)p Fn(T)1701 912 y Ff(\027)s
Fm(+1)1830 795 y Fp(Q)1902 758 y Fo(0)1902 818 y Fn(k)1939
827 y Fm(1)1973 818 y Fn(k)2010 827 y Fm(2)2049 795 y
Fp(e)2091 758 y Fn(i)p Fx(h)p Fn(k)2179 767 y Fm(1)2214
758 y Fn(;)p Fo(\012)2285 767 y Fm(1)2319 758 y Fx(i)p
Fn(t)p Fo(+)p Fn(i)p Fx(h)p Fn(k)2514 767 y Fm(2)2550
758 y Fn(;)p Fo(\012)2621 767 y Fm(2)2655 758 y Fx(i)p
Fn(')2728 766 y Ff(\027)2771 795 y Fp(:)165 1092 y Fv(Omitting)30
b(all)g(the)g(smaller)g(terms)f(of)h(order)f Fp(O)s Fv(\()p
Fp(I)1891 1106 y Fn(\027)1934 1092 y Fv(\),)i(the)e(functions)g
Fp(f)2616 1106 y Fn(\027)t Fo(0)2694 1092 y Fp(;)15 b(f)2779
1106 y Fn(\027)t Fo(1)2887 1092 y Fv(and)29 b Fp(g)3106
1106 y Fn(\027)t Fo(0)3214 1092 y Fv(in)g(the)h(trans-)165
1205 y(formation)h(\(2.11\))h(are)f(determined)f(b)m(y)g(the)h
(equations)660 1386 y Fp(@)5 b(f)758 1400 y Fn(\027)t(j)p
660 1427 174 4 v 703 1510 a Fp(@)g(t)863 1448 y Fv(+)1000
1386 y Fp(@)g(f)1098 1400 y Fn(\027)t(j)p 964 1427 247
4 v 964 1510 a Fp(@)g(')1076 1524 y Fn(\027)t Fo(+1)1220
1448 y Fp(a)1268 1462 y Fn(\027)t Fo(+1)1427 1448 y Fv(=)25
b Fp(R)1593 1400 y Fn(T)1634 1409 y Ff(\027)s Fm(+1)1592
1474 y Fn(\027)t(j)1753 1448 y Fp(;)1894 1386 y(@)5 b(g)1990
1400 y Fn(\027)t Fo(0)p 1894 1427 176 4 v 1939 1510 a
Fp(@)g(t)2100 1448 y Fv(+)2236 1386 y Fp(@)g(g)2332 1400
y Fn(\027)t Fo(0)p 2201 1427 247 4 v 2201 1510 a Fp(@)g(')2313
1524 y Fn(\027)t Fo(+1)2457 1448 y Fp(a)2505 1462 y Fn(\027)t
Fo(+1)2663 1448 y Fv(=)25 b Fp(Q)2831 1400 y Fn(T)2872
1409 y Ff(\027)s Fm(+1)2831 1473 y Fn(\027)t Fo(0)3012
1448 y Fv(+)20 b Fp(\033)3155 1462 y Fn(\027)3198 1448
y Fp(:)253 b Fv(\(2.16\))165 1719 y(Since)26 b(the)g(functions)g
Fp(R)1007 1733 y Fn(\027)t(j)1109 1719 y Fv(are)g(o)s(dd,)g(it)h(follo)
m(ws)g(that)g(a)m(v)r(\()p Fp(R)2228 1672 y Fn(T)2269
1681 y Ff(\027)s Fm(+1)2227 1745 y Fn(\027)t(j)2389 1719
y Fv(\))f(=)f(0.)39 b(W)-8 b(e)28 b(tak)m(e)f Fp(\033)3052
1733 y Fn(\027)3121 1719 y Fv(=)e(a)m(v)r(\()p Fq(\000)p
Fp(Q)3487 1672 y Fn(T)3528 1681 y Ff(\027)s Fm(+1)3487
1744 y Fn(\027)t Fo(0)3648 1719 y Fv(\).)165 1832 y(Hence,)31
b(from)f(\(2.16\))j(w)m(e)e(get)315 2039 y Fp(i)15 b
Fv(\()q Fq(h)p Fp(k)479 2053 y Fo(1)519 2039 y Fp(;)g
Fv(\012)625 2053 y Fo(1)664 2039 y Fq(i)21 b Fv(+)f Fq(h)p
Fp(k)893 2053 y Fo(2)933 2039 y Fp(;)15 b(a)1021 2053
y Fn(\027)t Fo(+1)1155 2039 y Fv(\012)1221 2053 y Fo(2)1260
2039 y Fq(i)p Fv(\))h Fp(f)1401 1995 y Fn(j)1391 2067
y(k)1428 2076 y Fm(1)1462 2067 y Fn(;k)1519 2076 y Fm(2)1640
2039 y Fv(=)83 b Fp(R)1864 1995 y Fn(j)1863 2067 y(k)1900
2076 y Fm(1)1934 2067 y Fn(;k)1991 2076 y Fm(2)2029 2039
y Fp(;)177 b(j)31 b Fv(=)25 b(1)p Fp(;)15 b Fv(2)p Fp(;)175
b Fv(0)26 b Fp(<)f Fq(j)p Fp(k)s Fq(j)h(\024)f Fp(T)3167
2053 y Fn(\027)t Fo(+1)3300 2039 y Fp(;)316 2272 y(i)15
b Fv(\()q Fq(h)p Fp(k)480 2286 y Fo(1)520 2272 y Fp(;)g
Fv(\012)626 2286 y Fo(1)666 2272 y Fq(i)20 b Fv(+)g Fq(h)p
Fp(k)894 2286 y Fo(2)934 2272 y Fp(;)15 b(a)1022 2286
y Fn(\027)t Fo(+1)1156 2272 y Fv(\012)1222 2286 y Fo(2)1261
2272 y Fq(i)p Fv(\))h Fp(g)1393 2239 y Fo(0)1390 2298
y Fn(k)1427 2307 y Fm(1)1462 2298 y Fn(;k)1519 2307 y
Fm(2)1640 2272 y Fv(=)83 b Fp(Q)1866 2239 y Fo(0)1866
2298 y Fn(k)1903 2307 y Fm(1)1937 2298 y Fn(;k)1994 2307
y Fm(2)2032 2272 y Fp(;)668 b Fv(0)26 b Fp(<)f Fq(j)p
Fp(k)s Fq(j)h(\024)f Fp(T)3167 2286 y Fn(\027)t Fo(+1)3300
2272 y Fp(;)3476 2154 y Fv(\(2.17\))165 2470 y(and)30
b(c)m(ho)s(ose)1335 2583 y Fp(f)1390 2546 y Fo(1)1380
2606 y(0)p Fn(;)p Fo(0)1499 2583 y Fv(=)25 b(0)p Fp(;)107
b(f)1827 2546 y Fo(2)1817 2606 y(0)p Fn(;)p Fo(0)1936
2583 y Fv(=)25 b(0)p Fp(;)107 b(g)2252 2597 y Fo(0)p
Fn(;)p Fo(0)2371 2583 y Fv(=)25 b(0)p Fp(:)165 2748 y
Fv(W)-8 b(e)31 b(note)g(that)393 2949 y Fq(jh)p Fp(k)500
2963 y Fo(1)540 2949 y Fp(;)15 b Fv(\012)646 2963 y Fo(1)686
2949 y Fq(i)20 b Fv(+)g Fq(h)p Fp(k)914 2963 y Fo(2)954
2949 y Fp(;)15 b(a)1042 2963 y Fn(\027)t Fo(+1)1176 2949
y Fv(\012)1242 2963 y Fo(2)1281 2949 y Fq(ij)84 b(\025)f(jh)p
Fp(k)1686 2963 y Fo(1)1726 2949 y Fp(;)15 b Fv(\012)1832
2963 y Fo(1)1872 2949 y Fq(i)20 b Fv(+)g Fq(h)p Fp(k)2100
2963 y Fo(2)2140 2949 y Fp(;)15 b(\013)p Fv(\012)2304
2963 y Fo(2)2344 2949 y Fq(ij)21 b(\000)f(jh)p Fp(k)2623
2963 y Fo(2)2663 2949 y Fp(;)15 b Fv(\()p Fp(a)2786 2963
y Fn(\027)t Fo(+1)2941 2949 y Fq(\000)k Fp(\013)p Fv(\)\012)3190
2963 y Fo(2)3230 2949 y Fq(ij)1425 3105 y(\025)83 b Fp(\015)5
b Fv(\010\()p Fq(j)p Fp(k)s Fq(j)p Fv(\))21 b Fq(\000)f
Fp(T)2032 3119 y Fn(\027)t Fo(+1)2165 3105 y Fp(h)2217
3119 y Fn(\027)t Fo(+1)2376 3105 y Fp(>)25 b(\015)5 b
Fv(\010\()p Fp(T)2678 3119 y Fn(\027)t Fo(+1)2812 3105
y Fv(\))21 b Fq(\000)3032 3044 y Fp(\015)p 2968 3084
179 4 v 2968 3168 a Fv(2)3013 3141 y Fn(\027)t Fo(+1)3157
3105 y Fv(\010\()p Fp(T)3311 3119 y Fn(\027)t Fo(+1)3445
3105 y Fv(\))1425 3302 y Fp(>)1589 3240 y(\015)p 1589
3280 53 4 v 1592 3364 a Fv(2)1651 3302 y(\010\()p Fp(T)1805
3316 y Fn(\027)t Fo(+1)1938 3302 y Fv(\))165 3528 y(when)36
b(0)i Fp(<)e Fq(j)p Fp(k)s Fq(j)i(\024)e Fp(T)897 3542
y Fn(\027)t Fo(+1)1068 3528 y Fv(and)h Fp(a)1300 3542
y Fn(\027)t Fo(+1)1470 3528 y Fq(2)g Fp(A)1636 3542 y
Fn(\015)1705 3528 y Fv(+)25 b Fp(h)1853 3542 y Fn(\027)t
Fo(+1)1986 3528 y Fv(,)40 b(for)d(an)g(appropriate)h
Fp(\013)f Fq(2)f Fp(A)3088 3542 y Fn(\015)3133 3528 y
Fv(.)62 b(Hence,)40 b(b)s(oth)165 3641 y(equations)28
b(in)f(\(2.16\))j(are)e(solv)-5 b(able.)40 b(It)28 b(also)g(follo)m(ws)
h(from)e(\(2.16\))j(that)e(the)f(functions)g Fp(f)3280
3655 y Fn(\027)t(j)3383 3641 y Fv(are)g(ev)m(en)165 3754
y(and)33 b Fp(g)388 3768 y Fn(\027)t Fo(0)501 3754 y
Fv(is)h(o)s(dd.)50 b(By)34 b(\(2.14\))i(and)d(\(2.15\),)k(w)m(e)d(see)h
(that)f(the)g(functions)g Fp(R)2818 3768 y Fn(\027)t
Fo(+1)2985 3754 y Fv(and)f Fp(Q)3237 3768 y Fn(\027)t
Fo(+1)3404 3754 y Fv(are)h(o)s(dd)165 3867 y(and)c(ev)m(en,)h(resp)s
(ectiv)m(ely)-8 b(.)42 b(F)-8 b(rom)31 b(\(1.8\))h(and)e(\(2.17\))j(w)m
(e)e(ha)m(v)m(e,)h(for)e(0)25 b Fp(<)g Fq(j)p Fp(k)s
Fq(j)h(\024)f Fp(T)2942 3881 y Fn(\027)t Fo(+1)730 4105
y Fq(j)p Fp(f)810 4068 y Fo(0)800 4128 y Fn(k)837 4137
y Fm(1)871 4128 y Fn(;k)928 4137 y Fm(2)967 4105 y Fq(j)83
b(\024)1403 4044 y Fv(2)p 1239 4084 375 4 v 1239 4168
a Fp(\015)5 b Fv(\010\()p Fp(T)1445 4182 y Fn(\027)t
Fo(+1)1578 4168 y Fv(\))1623 4105 y Fq(j)p Fp(R)1718
4068 y Fo(0)1717 4128 y Fn(k)1754 4137 y Fm(1)1789 4128
y Fn(;k)1846 4137 y Fm(2)1884 4105 y Fq(j)26 b(\024)2205
4044 y Fv(2)p 2041 4084 V 2041 4168 a Fp(\015)5 b Fv(\010\()p
Fp(T)2247 4182 y Fn(\027)t Fo(+1)2380 4168 y Fv(\))2425
4105 y Fq(j)p Fp(R)2519 4119 y Fn(\027)t Fo(0)2598 4105
y Fq(j)2623 4120 y Fn(r)2655 4128 y Ff(\027)2694 4120
y Fn(;s)2747 4128 y Ff(\027)2785 4120 y Fn(;h)2846 4128
y Ff(\027)2888 4105 y Fp(e)2930 4068 y Fx(\000j)p Fn(k)r
Fx(j)p Fn(r)3096 4076 y Ff(\027)1075 4344 y Fq(\024)1403
4282 y Fv(2)p 1239 4323 V 1239 4406 a Fp(\015)g Fv(\010\()p
Fp(T)1445 4420 y Fn(\027)t Fo(+1)1578 4406 y Fv(\))1623
4344 y Fq(j)p Fp(R)1717 4358 y Fn(\027)1761 4344 y Fq(j)1786
4359 y Fn(r)1818 4367 y Ff(\027)1857 4359 y Fn(;s)1910
4367 y Ff(\027)1947 4359 y Fn(;h)2008 4367 y Ff(\027)2050
4344 y Fp(e)2092 4306 y Fx(\000j)p Fn(k)r Fx(j)p Fn(r)2258
4314 y Ff(\027)2300 4344 y Fp(;)730 4635 y Fq(j)p Fp(f)810
4597 y Fo(1)800 4657 y Fn(k)837 4666 y Fm(1)871 4657
y Fn(;k)928 4666 y Fm(2)967 4635 y Fq(j)83 b(\024)1403
4573 y Fv(2)p 1239 4614 V 1239 4697 a Fp(\015)5 b Fv(\010\()p
Fp(T)1445 4711 y Fn(\027)t Fo(+1)1578 4697 y Fv(\))1623
4635 y Fq(j)p Fp(R)1718 4597 y Fo(1)1717 4657 y Fn(k)1754
4666 y Fm(1)1789 4657 y Fn(;k)1846 4666 y Fm(2)1884 4635
y Fq(j)26 b(\024)2205 4573 y Fv(2)p 2041 4614 V 2041
4697 a Fp(\015)5 b Fv(\010\()p Fp(T)2247 4711 y Fn(\027)t
Fo(+1)2380 4697 y Fv(\))2425 4635 y Fq(j)p Fp(R)2519
4649 y Fn(\027)t Fo(1)2598 4635 y Fq(j)2623 4650 y Fn(r)2655
4658 y Ff(\027)2694 4650 y Fn(;s)2747 4658 y Ff(\027)2785
4650 y Fn(;h)2846 4658 y Ff(\027)2888 4635 y Fp(e)2930
4597 y Fx(\000j)p Fn(k)r Fx(j)p Fn(r)3096 4605 y Ff(\027)1075
4873 y Fq(\024)1446 4812 y Fv(2)p 1239 4852 461 4 v 1239
4936 a Fp(\015)g(s)1334 4950 y Fn(\027)1376 4936 y Fv(\010\()p
Fp(T)1530 4950 y Fn(\027)t Fo(+1)1664 4936 y Fv(\))1709
4873 y Fq(j)p Fp(R)1803 4887 y Fn(\027)1847 4873 y Fq(j)1872
4888 y Fn(r)1904 4896 y Ff(\027)1942 4888 y Fn(;s)1995
4896 y Ff(\027)2033 4888 y Fn(;h)2094 4896 y Ff(\027)2136
4873 y Fp(e)2178 4836 y Fx(\000j)p Fn(k)r Fx(j)p Fn(r)2344
4844 y Ff(\027)2385 4873 y Fp(;)732 5164 y Fq(j)p Fp(g)803
5127 y Fo(0)800 5187 y Fn(k)837 5196 y Fm(1)871 5187
y Fn(;k)928 5196 y Fm(2)967 5164 y Fq(j)83 b(\024)1403
5103 y Fv(2)p 1239 5143 375 4 v 1239 5227 a Fp(\015)5
b Fv(\010\()p Fp(T)1445 5241 y Fn(\027)t Fo(+1)1578 5227
y Fv(\))1623 5164 y Fq(j)p Fp(Q)1720 5127 y Fo(0)1720
5187 y Fn(k)1757 5196 y Fm(1)1792 5187 y Fn(;k)1849 5196
y Fm(2)1887 5164 y Fq(j)25 b(\024)2208 5103 y Fv(2)p
2043 5143 V 2043 5227 a Fp(\015)5 b Fv(\010\()p Fp(T)2249
5241 y Fn(\027)t Fo(+1)2383 5227 y Fv(\))2428 5164 y
Fq(j)p Fp(Q)2525 5178 y Fn(\027)t Fo(0)2604 5164 y Fq(j)2629
5179 y Fn(r)2661 5187 y Ff(\027)2700 5179 y Fn(;s)2753
5187 y Ff(\027)2790 5179 y Fn(;h)2851 5187 y Ff(\027)2893
5164 y Fp(e)2935 5127 y Fx(\000j)p Fn(k)r Fx(j)p Fn(r)3101
5135 y Ff(\027)1075 5403 y Fq(\024)1403 5341 y Fv(2)p
1239 5382 V 1239 5465 a Fp(\015)g Fv(\010\()p Fp(T)1445
5479 y Fn(\027)t Fo(+1)1578 5465 y Fv(\))1623 5403 y
Fq(j)p Fp(Q)1720 5417 y Fn(\027)1764 5403 y Fq(j)1789
5418 y Fn(r)1821 5426 y Ff(\027)1859 5418 y Fn(;s)1912
5426 y Ff(\027)1950 5418 y Fn(;h)2011 5426 y Ff(\027)2053
5403 y Fp(e)2095 5365 y Fx(\000j)p Fn(k)r Fx(j)p Fn(r)2261
5373 y Ff(\027)2302 5403 y Fp(:)1914 5691 y Fv(8)p eop
end
%%Page: 9 9
TeXDict begin 9 8 bop 165 337 a Fv(Hence,)31 b(it)g(follo)m(ws)h(from)e
(\(2.12\))i(and)e(\(2.13\))j(that)165 535 y Fq(j)p Fp(I)230
549 y Fn(\027)293 535 y Fq(\000)20 b Fp(I)424 549 y Fn(\027)t
Fo(+1)558 535 y Fq(j)25 b Fv(=)g Fq(j)p Fp(f)774 549
y Fn(\027)t Fo(0)852 535 y Fv(\()p Fp(')946 549 y Fn(\027)t
Fo(+1)1081 535 y Fp(;)15 b(t;)g(a)1242 549 y Fn(\027)t
Fo(+1)1376 535 y Fv(\))p Fq(j)20 b Fv(+)g Fq(j)p Fp(f)1617
549 y Fn(\027)t Fo(1)1696 535 y Fv(\()p Fp(')1790 549
y Fn(\027)t Fo(+1)1924 535 y Fp(;)15 b(t;)g(a)2085 549
y Fn(\027)t Fo(+1)2219 535 y Fv(\))p Fq(jj)p Fp(I)2344
549 y Fn(\027)t Fo(+1)2478 535 y Fq(j)248 810 y(\024)486
730 y Fg(X)402 918 y Fx(j)p Fn(k)r Fx(j\024)p Fn(T)577
927 y Ff(\027)s Fm(+1)706 810 y Fq(j)p Fp(f)786 773 y
Fo(0)776 833 y Fn(k)813 842 y Fm(1)847 833 y Fn(;k)904
842 y Fm(2)942 810 y Fq(j)967 825 y Fn(r)999 833 y Ff(\027)1038
825 y Fn(;s)1091 833 y Ff(\027)1129 825 y Fn(;h)1190
833 y Ff(\027)1231 810 y Fp(e)1273 773 y Fx(\000j)p Fn(k)r
Fx(j)p Fo(\()p Fn(r)1466 781 y Ff(\027)1504 773 y Fx(\000)p
Fn(r)1591 782 y Ff(\027)s Fm(+1)1706 773 y Fo(\))1758
810 y Fv(+)20 b Fp(s)1892 824 y Fn(\027)t Fo(+1)2125
730 y Fg(X)2040 918 y Fx(j)p Fn(k)r Fx(j\024)p Fn(T)2215
927 y Ff(\027)s Fm(+1)2345 810 y Fq(j)p Fp(f)2425 773
y Fo(1)2415 833 y Fn(k)2452 842 y Fm(1)2486 833 y Fn(;k)2543
842 y Fm(2)2581 810 y Fq(j)2606 825 y Fn(r)2638 833 y
Ff(\027)2676 825 y Fn(;s)2729 833 y Ff(\027)2767 825
y Fn(;h)2828 833 y Ff(\027)2870 810 y Fp(e)2912 773 y
Fx(\000j)p Fn(k)r Fx(j)p Fo(\()p Fn(r)3105 781 y Ff(\027)3143
773 y Fx(\000)p Fn(r)3230 782 y Ff(\027)s Fm(+1)3345
773 y Fo(\))248 1129 y Fq(\024)486 1048 y Fg(X)402 1237
y Fx(j)p Fn(k)r Fx(j\024)p Fn(T)577 1246 y Ff(\027)s
Fm(+1)881 1068 y Fv(2)p 716 1108 375 4 v 716 1192 a Fp(\015)5
b Fv(\010\()p Fp(T)922 1206 y Fn(\027)t Fo(+1)1056 1192
y Fv(\))1101 1129 y Fq(j)p Fp(R)1195 1143 y Fn(\027)1238
1129 y Fq(j)1263 1144 y Fn(r)1295 1152 y Ff(\027)1334
1144 y Fn(;s)1387 1152 y Ff(\027)1425 1144 y Fn(;h)1486
1152 y Ff(\027)1528 1129 y Fp(e)1570 1092 y Fx(\000j)p
Fn(k)r Fx(j)p Fo(\()p Fn(r)1763 1100 y Ff(\027)1800 1092
y Fx(\000)p Fn(r)1887 1101 y Ff(\027)s Fm(+1)2003 1092
y Fo(\))2054 1129 y Fv(+)20 b Fp(s)2188 1143 y Fn(\027)t
Fo(+1)2421 1048 y Fg(X)2336 1237 y Fx(j)p Fn(k)r Fx(j\024)p
Fn(T)2511 1246 y Ff(\027)s Fm(+1)2858 1068 y Fv(2)p 2651
1108 461 4 v 2651 1192 a Fp(\015)5 b(s)2746 1206 y Fn(\027)2789
1192 y Fv(\010\()p Fp(T)2943 1206 y Fn(\027)t Fo(+1)3076
1192 y Fv(\))3122 1129 y Fq(j)p Fp(R)3216 1143 y Fn(\027)3259
1129 y Fq(j)3284 1144 y Fn(r)3316 1152 y Ff(\027)3355
1144 y Fn(;s)3408 1152 y Ff(\027)3445 1144 y Fn(;h)3506
1152 y Ff(\027)3548 1129 y Fp(e)3590 1092 y Fx(\000j)p
Fn(k)r Fx(j)p Fo(\()p Fn(r)3783 1100 y Ff(\027)3821 1092
y Fx(\000)p Fn(r)3908 1101 y Ff(\027)s Fm(+1)4023 1092
y Fo(\))248 1481 y Fq(\024)412 1420 y Fv(2)p Fp(s)500
1434 y Fn(\027)543 1420 y Fv(\()p Fp(s)621 1434 y Fn(\027)684
1420 y Fv(+)20 b Fp(s)818 1434 y Fn(\027)t Fo(+1)951
1420 y Fv(\))p 412 1460 575 4 v 538 1543 a(\010\()p Fp(T)692
1557 y Fn(\027)t Fo(+1)825 1543 y Fv(\))996 1481 y(\()p
Fp(N)1104 1495 y Fo(1)1164 1481 y Fv(+)g Fp(N)1328 1495
y Fo(2)1368 1481 y Fv(\)!4)1473 1444 y Fn(N)1529 1453
y Fm(1)1564 1444 y Fo(+)p Fn(N)1675 1453 y Fm(2)1729
1362 y Fg(\022)1800 1420 y Fv(2\()p Fp(N)1953 1434 y
Fo(1)2014 1420 y Fv(+)g Fp(N)2178 1434 y Fo(2)2217 1420
y Fv(\))p 1800 1460 453 4 v 1933 1543 a Fp(T)1986 1557
y Fn(\027)t Fo(+1)2278 1481 y Fv(log)2420 1420 y(4\()p
Fp(N)2573 1434 y Fo(1)2634 1420 y Fv(+)g Fp(N)2798 1434
y Fo(2)2837 1420 y Fv(\))p 2420 1460 V 2619 1543 a Fp(\026)2882
1362 y Fg(\023)2944 1378 y Fx(\000)p Fo(\()p Fn(N)3082
1387 y Fm(1)3116 1378 y Fo(+)p Fn(N)3227 1387 y Fm(2)3262
1378 y Fo(\))3823 1481 y Fv(\(2.18\))248 1804 y Fq(\024)412
1738 y Fv(2)p Fp(s)500 1752 y Fn(\027)543 1738 y Fv(\()p
Fp(s)621 1752 y Fn(\027)684 1738 y Fv(+)g Fp(s)818 1752
y Fn(\027)t Fo(+1)951 1738 y Fv(\)\()p Fp(N)1094 1752
y Fo(1)1154 1738 y Fv(+)g Fp(N)1318 1752 y Fo(2)1358
1738 y Fv(\)!4)1463 1705 y Fn(N)1519 1714 y Fm(1)1554
1705 y Fo(+)p Fn(N)1665 1714 y Fm(2)1704 1738 y Fp(T)1770
1697 y Fn(N)1826 1706 y Fm(1)1860 1697 y Fo(+)p Fn(N)1971
1706 y Fm(2)1757 1763 y Fn(\027)t Fo(+1)p 412 1783 1599
4 v 954 1866 a Fp(T)1020 1835 y Fn($)1007 1891 y(\027)t
Fo(+1)1140 1866 y Fv(\011\()p Fp(T)1299 1880 y Fn(\027)t
Fo(+1)1433 1866 y Fv(\))2045 1804 y Fq(\024)25 b Fv(2)p
Fp(c)2225 1818 y Fo(1)2266 1804 y Fp(s)2309 1766 y Fo(2)2348
1804 y Fp(\026)2403 1766 y Fo(\(2)p Fn(\024)p Fx(\000)p
Fn(\034)8 b Fo(\))p Fn(\027)t Fx(\000)p Fn(\034)2789
1804 y Fq(\024)25 b Fv(2)p Fp(c)2969 1818 y Fo(1)3010
1804 y Fp(s)3053 1766 y Fo(2)3092 1804 y Fp(\026)3147
1766 y Fn(\024\027)t Fx(\000)p Fn(\034)248 2054 y Fq(\024)83
b Fv(2)p Fp(c)486 2068 y Fo(1)526 2054 y Fp(s)584 1935
y Fg(\024)677 1992 y Fv(1)p 637 2033 125 4 v 637 2116
a(2)p Fp(c)721 2130 y Fo(1)772 2054 y Fv(\(1)21 b Fq(\000)e
Fp(\026)1018 2016 y Fn(\024)1063 2054 y Fv(\))p Fp(\026)1153
2016 y Fn(\024)1198 1935 y Fg(\025)1257 2054 y Fp(\026)1312
2016 y Fn(\024\027)t Fx(\000)p Fn(\034)1515 2054 y Fv(=)25
b Fp(s\026)1709 2016 y Fn(\024\027)1812 2054 y Fq(\000)20
b Fp(s\026)2001 2016 y Fn(\024)p Fo(\()p Fn(\027)t Fo(+1\))2255
2054 y Fv(=)25 b Fp(s)2394 2068 y Fn(\027)2457 2054 y
Fq(\000)19 b Fp(s)2590 2068 y Fn(\027)t Fo(+1)165 2287
y Fv(and)250 2485 y Fq(j)p Fp(')334 2499 y Fn(\027)398
2485 y Fq(\000)h Fp(')548 2499 y Fn(\027)t Fo(+1)682
2485 y Fq(j)25 b Fv(=)g Fq(j)p Fp(g)896 2499 y Fn(\027)t
Fo(0)975 2485 y Fv(\()p Fp(')1069 2499 y Fn(\027)t Fo(+1)1203
2485 y Fp(;)15 b(t;)g(a)1364 2499 y Fn(\027)t Fo(+1)1498
2485 y Fv(\))p Fq(j)26 b(\024)1765 2405 y Fg(X)1680 2593
y Fx(j)p Fn(k)r Fx(j\024)p Fn(T)1855 2602 y Ff(\027)s
Fm(+1)1985 2485 y Fq(j)p Fp(g)2056 2448 y Fo(0)2053 2508
y Fn(k)2090 2517 y Fm(1)2124 2508 y Fn(;k)2181 2517 y
Fm(2)2220 2485 y Fq(j)2245 2500 y Fn(r)2277 2508 y Ff(\027)2315
2500 y Fn(;s)2368 2508 y Ff(\027)2406 2500 y Fn(;h)2467
2508 y Ff(\027)2509 2485 y Fp(e)2551 2448 y Fx(\000j)p
Fn(k)r Fx(j)p Fo(\()p Fn(r)2744 2456 y Ff(\027)2782 2448
y Fx(\000)p Fn(r)2869 2457 y Ff(\027)s Fm(+1)2984 2448
y Fo(\))333 2804 y Fq(\024)571 2723 y Fg(X)486 2911 y
Fx(j)p Fn(k)r Fx(j\024)p Fn(T)661 2920 y Ff(\027)s Fm(+1)966
2743 y Fv(2)p 801 2783 375 4 v 801 2866 a Fp(\015)5 b
Fv(\010\()p Fp(T)1007 2880 y Fn(\027)t Fo(+1)1140 2866
y Fv(\))1186 2804 y Fq(j)p Fp(Q)1283 2818 y Fn(\027)1326
2804 y Fq(j)1351 2819 y Fn(r)1383 2827 y Ff(\027)1422
2819 y Fn(;s)1475 2827 y Ff(\027)1512 2819 y Fn(;h)1573
2827 y Ff(\027)1615 2804 y Fp(e)1657 2767 y Fx(\000j)p
Fn(k)r Fx(j)p Fo(\()p Fn(r)1850 2775 y Ff(\027)1888 2767
y Fx(\000)p Fn(r)1975 2776 y Ff(\027)s Fm(+1)2090 2767
y Fo(\))3476 2804 y Fv(\(2.19\))333 3156 y Fq(\024)661
3094 y Fv(2)p 496 3135 V 496 3218 a Fp(\015)g Fv(\010\()p
Fp(T)702 3232 y Fn(\027)t Fo(+1)836 3218 y Fv(\))881
3156 y Fq(j)p Fp(Q)978 3170 y Fn(\027)1022 3156 y Fq(j)1047
3171 y Fn(r)1079 3179 y Ff(\027)1117 3171 y Fn(;s)1170
3179 y Ff(\027)1208 3171 y Fn(;h)1269 3179 y Ff(\027)1311
3156 y Fv(\()p Fp(N)1419 3170 y Fo(1)1479 3156 y Fv(+)20
b Fp(N)1643 3170 y Fo(2)1682 3156 y Fv(\)!4)1787 3118
y Fn(N)1843 3127 y Fm(1)1879 3118 y Fo(+)p Fn(N)1990
3127 y Fm(2)2044 3037 y Fg(\022)2115 3094 y Fv(2\()p
Fp(N)2268 3108 y Fo(1)2328 3094 y Fv(+)g Fp(N)2492 3108
y Fo(2)2532 3094 y Fv(\))p 2115 3135 453 4 v 2248 3218
a Fp(T)2301 3232 y Fn(\027)t Fo(+1)2592 3156 y Fv(log)2735
3094 y(4\()p Fp(N)2888 3108 y Fo(1)2948 3094 y Fv(+)g
Fp(N)3112 3108 y Fo(2)3152 3094 y Fv(\))p 2735 3135 V
2934 3218 a Fp(\026)3197 3037 y Fg(\023)3258 3053 y Fx(\000)p
Fo(\()p Fn(N)3396 3062 y Fm(1)3431 3053 y Fo(+)p Fn(N)3542
3062 y Fm(2)3577 3053 y Fo(\))333 3479 y Fq(\024)496
3413 y Fv(2\()p Fp(N)649 3427 y Fo(1)710 3413 y Fv(+)g
Fp(N)874 3427 y Fo(2)913 3413 y Fv(\)!4)1018 3380 y Fn(N)1074
3389 y Fm(1)1110 3380 y Fo(+)p Fn(N)1221 3389 y Fm(2)1260
3413 y Fp(s)1303 3427 y Fn(\027)1345 3413 y Fp(T)1411
3372 y Fn(N)1467 3381 y Fm(1)1502 3372 y Fo(+)p Fn(N)1613
3381 y Fm(2)1398 3438 y Fn(\027)t Fo(+1)p 496 3458 1155
4 v 817 3541 a Fp(T)883 3510 y Fn($)870 3566 y(\027)t
Fo(+1)1003 3541 y Fv(\011\()p Fp(T)1162 3555 y Fn(\027)t
Fo(+1)1296 3541 y Fv(\))1687 3479 y Fq(\024)2062 3417
y Fp(c)2101 3431 y Fo(1)2141 3417 y Fp(s)2184 3431 y
Fn(\027)p 1793 3458 704 4 v 1793 3554 a Fp(T)1859 3513
y Fn($)r Fx(\000)p Fn(N)2031 3522 y Fm(1)2064 3513 y
Fx(\000)p Fn(N)2175 3522 y Fm(2)1846 3579 y Fn(\027)t
Fo(+1)2214 3554 y Fp(\026)2269 3527 y Fn(\034)8 b Fo(\()p
Fn(\027)t Fo(+1\))333 3785 y Fq(\024)496 3723 y Fp(c)535
3737 y Fo(1)575 3723 y Fp(s\026)673 3690 y Fn(\024)p
Fx(\000)p Fn(\034)p 496 3764 315 4 v 512 3847 a Fp(T)565
3861 y Fn(\027)t Fo(+1)698 3847 y Fp(\026)753 3821 y
Fn(\034)847 3785 y Fq(\024)989 3723 y Fp(c)1028 3737
y Fo(1)1068 3723 y Fp(s)p 952 3764 195 4 v 952 3847 a(T)1005
3861 y Fn(\027)1049 3847 y Fp(\026)1104 3821 y Fn(\034)1182
3785 y Fq(\024)1343 3723 y Fv(1)p 1288 3764 157 4 v 1288
3847 a Fp(!)s(T)1401 3861 y Fn(\027)165 4024 y Fv(pro)m(vided)30
b(that)1246 4173 y(0)c Fp(<)f(s)f(<)h Fv(min)1743 4054
y Fg(\032)1855 4112 y Fv(1)p 1815 4152 125 4 v 1815 4236
a(2)p Fp(c)1899 4250 y Fo(1)1950 4173 y Fv(\()p Fp(\026)2040
4136 y Fn(\024)2105 4173 y Fq(\000)20 b Fp(\026)2251
4136 y Fo(2)p Fn(\024)2330 4173 y Fv(\);)2437 4112 y
Fp(\026)2492 4079 y Fn(\034)p 2416 4152 139 4 v 2416
4236 a Fp(c)2455 4250 y Fo(1)2495 4236 y Fp(!)2565 4054
y Fg(\033)165 4373 y Fv(where)390 4606 y Fp(c)429 4620
y Fo(1)494 4606 y Fv(:=)625 4544 y(2\()p Fp(N)778 4558
y Fo(1)838 4544 y Fv(+)g Fp(N)1002 4558 y Fo(2)1042 4544
y Fv(\)!4)1147 4511 y Fn(N)1203 4520 y Fm(1)1238 4511
y Fo(+)p Fn(N)1349 4520 y Fm(2)p 625 4585 764 4 v 889
4668 a Fv(\011\()p Fp(T)1048 4682 y Fo(0)1088 4668 y
Fv(\))1398 4606 y Fp(;)106 b(!)28 b Fv(:=)e(max)15 b
Fq(fj)p Fp(!)2047 4620 y Fo(1)2087 4606 y Fq(j)p Fp(;)g(:)g(:)g(:)i(;)e
Fq(j)p Fp(!)2396 4620 y Fn(N)2452 4629 y Fm(1)2491 4606
y Fq(j)p Fp(;)g Fq(j)p Fp(!)2638 4620 y Fn(N)2694 4629
y Fm(1)2729 4620 y Fo(+1)2823 4606 y Fq(j)p Fp(;)g(:)g(:)g(:)i(;)e
Fq(j)p Fp(!)3132 4620 y Fn(N)3188 4629 y Fm(1)3223 4620
y Fo(+)p Fn(N)3334 4629 y Fm(2)3372 4606 y Fq(jg)h Fp(:)165
4848 y Fv(Hence,)31 b(w)m(e)g(obtain)938 5046 y Fq(j)p
Fp(I)1003 5060 y Fn(\027)1047 5046 y Fq(j)25 b(\024)g(j)p
Fp(I)1258 5060 y Fn(\027)t Fo(+1)1392 5046 y Fq(j)20
b Fv(+)g Fq(j)p Fp(I)1593 5060 y Fn(\027)1657 5046 y
Fq(\000)g Fp(I)1788 5060 y Fn(\027)t Fo(+1)1921 5046
y Fq(j)26 b(\024)f Fp(s)2111 5060 y Fn(\027)t Fo(+1)2264
5046 y Fv(+)20 b Fp(s)2398 5060 y Fn(\027)2461 5046 y
Fq(\000)g Fp(s)2595 5060 y Fn(\027)t Fo(+1)2753 5046
y Fv(=)25 b Fp(s)2892 5060 y Fn(\027)165 5244 y Fv(and)665
5442 y Fq(j)15 b Fv(Im)836 5415 y Fg(e)829 5442 y Fp(\022)872
5456 y Fn(j)t(\027)947 5442 y Fq(j)84 b Fv(=)e Fq(j)15
b Fv(Im)g Fp(!)1430 5456 y Fn(j)1467 5442 y Fp(')1526
5456 y Fn(\027)1569 5442 y Fq(j)26 b(\024)f(j)15 b Fv(Im)g
Fp(!)1937 5456 y Fn(j)1973 5442 y Fp(')2032 5456 y Fn(\027)t
Fo(+1)2166 5442 y Fq(j)20 b Fv(+)g Fq(j)15 b Fv(Im)g
Fp(!)2523 5456 y Fn(j)2559 5442 y Fp(')2618 5456 y Fn(\027)2682
5442 y Fq(\000)20 b Fv(Im)15 b Fp(!)2954 5456 y Fn(j)2990
5442 y Fp(')3049 5456 y Fn(\027)t Fo(+1)3183 5442 y Fq(j)1914
5691 y Fv(9)p eop end
%%Page: 10 10
TeXDict begin 10 9 bop 1056 365 a Fq(\024)82 b(j)15 b
Fv(Im)g Fp(!)1430 379 y Fn(j)1467 365 y Fp(')1526 379
y Fn(\027)t Fo(+1)1659 365 y Fq(j)21 b Fv(+)f Fq(j)p
Fp(!)1878 379 y Fn(j)1914 365 y Fp(')1973 379 y Fn(\027)2037
365 y Fq(\000)g Fp(!)2185 379 y Fn(j)2221 365 y Fp(')2280
379 y Fn(\027)t Fo(+1)2414 365 y Fq(j)25 b(\024)g Fp(r)2601
379 y Fn(\027)t Fo(+1)2755 365 y Fv(+)2881 304 y(1)p
2856 344 97 4 v 2856 428 a Fp(T)2909 442 y Fn(\027)1056
604 y Fq(\024)82 b Fp(r)1250 618 y Fn(\027)t Fo(+1)1404
604 y Fv(+)1505 543 y(2\()p Fp(N)1658 557 y Fo(1)1718
543 y Fv(+)20 b Fp(N)1882 557 y Fo(2)1922 543 y Fv(\))p
1505 583 453 4 v 1683 667 a Fp(T)1736 681 y Fn(\027)1982
604 y Fv(log)2125 543 y(4\()p Fp(N)2278 557 y Fo(1)2338
543 y Fv(+)g Fp(N)2502 557 y Fo(2)2542 543 y Fv(\))p
2125 583 V 2323 667 a Fp(\026)2612 604 y Fv(=)25 b Fp(r)2749
618 y Fn(\027)2792 604 y Fp(:)165 847 y Fv(This)e(implies)i(that)f(the)
h(transformation)f Fq(S)1678 861 y Fn(\027)1746 847 y
Fv(de\014ned)f(b)m(y)h(\(2.11\))i(satis\014es)f Fq(S)2813
861 y Fn(\027)2856 847 y Fv(\()p Fp(D)2966 861 y Fn(r)2998
870 y Ff(\027)s Fm(+1)3114 861 y Fn(;s)3167 870 y Ff(\027)s
Fm(+1)3286 847 y Fv(\))g Fq(\032)g Fp(D)3517 861 y Fn(r)3549
869 y Ff(\027)3588 861 y Fn(;s)3641 869 y Ff(\027)3683
847 y Fv(.)165 960 y(Note)32 b(that)503 1184 y Fp(r)544
1198 y Fn(\027)608 1184 y Fq(\000)20 b Fp(r)740 1198
y Fn(\027)t Fo(+1)956 1184 y Fv(=)1120 1122 y(2\()p Fp(N)1273
1136 y Fo(1)1333 1122 y Fv(+)g Fp(N)1497 1136 y Fo(2)1537
1122 y Fv(\))p 1120 1163 V 1298 1246 a Fp(T)1351 1260
y Fn(\027)1597 1184 y Fv(log)1740 1122 y(4\()p Fp(N)1893
1136 y Fo(1)1953 1122 y Fv(+)g Fp(N)2117 1136 y Fo(2)2157
1122 y Fv(\))p 1740 1163 V 1938 1246 a Fp(\026)2227 1184
y Fq(\025)2333 1122 y Fv(\()p Fp(N)2441 1136 y Fo(1)2501
1122 y Fv(+)g Fp(N)2665 1136 y Fo(2)2704 1122 y Fv(\))p
2333 1163 407 4 v 2488 1246 a Fp(T)2541 1260 y Fn(\027)2765
1184 y Fv(log)2907 1122 y(4\()p Fp(N)3060 1136 y Fo(1)3121
1122 y Fv(+)g Fp(N)3285 1136 y Fo(2)3324 1122 y Fv(\))p
2907 1163 453 4 v 3106 1246 a Fp(\026)956 1417 y Fq(\025)1145
1356 y Fv(2)p 1120 1396 97 4 v 1120 1480 a Fp(T)1173
1494 y Fn(\027)1251 1417 y Fq(\025)1428 1356 y Fv(2)p
1357 1396 187 4 v 1357 1480 a Fp(T)1410 1494 y Fn(\027)t
Fo(+1)1554 1417 y Fp(;)165 1663 y Fv(it)31 b(follo)m(ws)g(from)f
(\(2.18\),)j(\(2.19\),)g(\(2.11\))g(and)c(the)i(second)f(inequalit)m(y)
i(of)f(\(1.8\))h(that)296 1862 y Fq(jS)376 1876 y Fn(\027)439
1862 y Fq(\000)20 b Fp(id)p Fq(j)84 b(\024)f(j)p Fp(f)941
1876 y Fn(\027)t Fo(0)1019 1862 y Fv(\()p Fp(')1113 1876
y Fn(\027)t Fo(+1)1247 1862 y Fp(;)15 b(t;)g(a)1408 1876
y Fn(\027)t Fo(+1)1542 1862 y Fv(\))p Fq(j)21 b Fv(+)f
Fq(j)p Fp(f)1784 1876 y Fn(\027)t Fo(1)1862 1862 y Fv(\()p
Fp(')1956 1876 y Fn(\027)t Fo(+1)2090 1862 y Fp(;)15
b(t;)g(a)2251 1876 y Fn(\027)t Fo(+1)2385 1862 y Fv(\))p
Fq(j)21 b(\001)g(j)p Fp(I)2577 1876 y Fn(\027)t Fo(+1)2710
1862 y Fq(j)g Fv(+)f Fq(j)p Fp(g)2915 1876 y Fn(\027)t
Fo(0)2994 1862 y Fv(\()p Fp(')3088 1876 y Fn(\027)t Fo(+1)3222
1862 y Fp(;)15 b(t;)g(a)3383 1876 y Fn(\027)t Fo(+1)3517
1862 y Fv(\))p Fq(j)717 2177 y(\024)83 b Fv(2)p Fp(c)955
2191 y Fo(1)995 2177 y Fp(s)1038 2139 y Fo(2)1077 2177
y Fp(\026)1132 2139 y Fn(\024\027)t Fx(\000)p Fn(\034)1330
2177 y Fv(+)1431 2115 y Fp(c)1470 2129 y Fo(1)1509 2115
y Fp(s\026)1607 2082 y Fo(\()p Fn(\024)p Fx(\000)p Fn(\034)8
b Fo(\))p Fn(\027)p 1431 2156 409 4 v 1493 2239 a Fp(T)1546
2253 y Fn(\027)t Fo(+1)1679 2239 y Fp(\026)1734 2213
y Fn(\034)1875 2177 y Fq(\024)25 b Fv(3)p Fp(c)2055 2191
y Fo(1)2095 2177 y Fp(s\026)2193 2139 y Fo(\()p Fn(\024)p
Fx(\000)p Fn(\034)8 b Fo(\))p Fn(\027)t Fx(\000)p Fn(\034)2544
2177 y Fq(\024)25 b Fp(c)2679 2191 y Fo(2)2719 2177 y
Fp(\026)2774 2139 y Fo(\()p Fn(\024)p Fx(\000)p Fn(\034)8
b Fo(\))p Fn(\027)3476 2177 y Fv(\(2.20\))165 2417 y(and)239
2632 y Fq(j)p Fp(D)s Fq(S)397 2646 y Fn(\027)461 2632
y Fq(\000)20 b Fp(I)7 b(d)p Fq(j)83 b(\024)g(j)p Fp(f)978
2646 y Fn(\027)t Fo(1)1056 2632 y Fq(j)21 b Fv(+)1365
2570 y(1)p 1203 2611 370 4 v 1203 2694 a Fp(r)1244 2708
y Fn(\027)1307 2694 y Fq(\000)f Fp(r)1439 2708 y Fn(\027)t
Fo(+1)1582 2632 y Fv(\()p Fq(j)p Fp(g)1685 2646 y Fn(\027)t
Fo(0)1765 2632 y Fq(j)g Fv(+)g Fq(j)p Fp(f)1971 2646
y Fn(\027)t Fo(0)2049 2632 y Fq(j)h Fv(+)f Fq(j)p Fp(f)2256
2646 y Fn(\027)t Fo(1)2334 2632 y Fq(jj)p Fp(I)2424 2646
y Fn(\027)t Fo(+1)2558 2632 y Fq(j)p Fv(\))754 2955 y
Fq(\024)918 2889 y Fv(2)p Fp(s)1006 2903 y Fn(\027)1049
2889 y Fv(\()p Fp(N)1157 2903 y Fo(1)1217 2889 y Fv(+)g
Fp(N)1381 2903 y Fo(2)1421 2889 y Fv(\)!4)1526 2856 y
Fn(N)1582 2865 y Fm(1)1617 2856 y Fo(+)p Fn(N)1728 2865
y Fm(2)1767 2889 y Fp(T)1833 2848 y Fn(N)1889 2857 y
Fm(1)1923 2848 y Fo(+)p Fn(N)2034 2857 y Fm(2)1820 2914
y Fn(\027)t Fo(+1)p 918 2934 1155 4 v 1238 3017 a Fp(T)1304
2986 y Fn($)1291 3042 y(\027)t Fo(+1)1425 3017 y Fv(\011\()p
Fp(T)1584 3031 y Fn(\027)t Fo(+1)1717 3017 y Fv(\))868
3278 y(+)1131 3216 y(1)p 969 3257 370 4 v 969 3340 a
Fp(r)1010 3354 y Fn(\027)1073 3340 y Fq(\000)g Fp(r)1205
3354 y Fn(\027)t Fo(+1)1363 3134 y Fg(")1422 3216 y Fp(c)1461
3230 y Fo(1)1501 3216 y Fp(s\026)1599 3183 y Fo(\()p
Fn(\024)p Fx(\000)p Fn(\034)8 b Fo(\))p Fn(\027)p 1422
3257 409 4 v 1484 3340 a Fp(T)1537 3354 y Fn(\027)t Fo(+1)1670
3340 y Fp(\026)1725 3314 y Fn(\034)1861 3278 y Fv(+)1962
3212 y(2)p Fp(s)2050 3226 y Fn(\027)2093 3212 y Fv(\()p
Fp(s)2171 3226 y Fn(\027)2234 3212 y Fv(+)20 b Fp(s)2368
3226 y Fn(\027)t Fo(+1)2501 3212 y Fv(\)\()p Fp(N)2644
3226 y Fo(1)2704 3212 y Fv(+)g Fp(N)2868 3226 y Fo(2)2908
3212 y Fv(\)!4)3013 3179 y Fn(N)3069 3188 y Fm(1)3105
3179 y Fo(+)p Fn(N)3216 3188 y Fm(2)3254 3212 y Fp(T)3320
3171 y Fn(N)3376 3180 y Fm(1)3411 3171 y Fo(+)p Fn(N)3522
3180 y Fm(2)3307 3237 y Fn(\027)t Fo(+1)p 1962 3257 1599
4 v 2504 3340 a Fp(T)2570 3309 y Fn($)2557 3365 y(\027)t
Fo(+1)2690 3340 y Fv(\011\()p Fp(T)2849 3354 y Fn(\027)t
Fo(+1)2983 3340 y Fv(\))3570 3134 y Fg(#)754 3593 y Fq(\024)918
3532 y Fp(c)957 3546 y Fo(1)997 3532 y Fp(s\026)1095
3499 y Fo(\()p Fn(\024)p Fx(\000)p Fn(\034)8 b Fo(\))p
Fn(\027)p 918 3572 409 4 v 1074 3656 a Fp(\026)1129 3629
y Fn(\034)1357 3593 y Fv(+)1458 3532 y Fp(c)1497 3546
y Fo(1)1537 3532 y Fp(s\026)1635 3499 y Fo(\()p Fn(\024)p
Fx(\000)p Fn(\034)g Fo(\))p Fn(\027)p 1458 3572 V 1613
3656 a Fp(\026)1668 3629 y Fn(\034)1897 3593 y Fv(+)1998
3532 y(2)p Fp(c)2082 3546 y Fo(1)2122 3532 y Fp(s\026)2220
3499 y Fo(\()p Fn(\024)p Fx(\000)p Fn(\034)g Fo(\))p
Fn(\027)p 1998 3572 455 4 v 2176 3656 a Fp(\026)2231
3629 y Fn(\034)3476 3593 y Fv(\(2.21\))754 3909 y Fq(\024)918
3847 y Fv(4)p Fp(c)1002 3861 y Fo(1)1042 3847 y Fp(s\026)1140
3814 y Fo(\()p Fn(\024)p Fx(\000)p Fn(\034)g Fo(\))p
Fn(\027)p 918 3887 V 1096 3971 a Fp(\026)1151 3945 y
Fn(\034)1408 3909 y Fq(\024)24 b Fp(c)1542 3923 y Fo(2)1582
3909 y Fp(\026)1637 3871 y Fo(\()p Fn(\024)p Fx(\000)p
Fn(\034)8 b Fo(\))p Fn(\027)1870 3909 y Fp(;)165 4163
y Fv(where)30 b Fp(c)467 4177 y Fo(2)532 4163 y Fv(:=)663
4126 y Fo(4)p Fn(c)729 4135 y Fm(1)p 663 4142 101 4 v
672 4194 a Fn(\026)714 4175 y Ff(\034)773 4163 y Fv(.)41
b(Moreo)m(v)m(er,)33 b(b)m(y)d(the)h(de\014nition)f(of)g
Fp(\033)2106 4177 y Fn(\027)2180 4163 y Fv(w)m(e)g(ha)m(v)m(e)447
4426 y Fq(j)p Fp(\033)524 4440 y Fn(\027)568 4426 y Fq(j)83
b Fv(=)g Fq(j)p Fv(a)m(v)r(\()p Fq(\000)p Fp(Q)1125 4378
y Fn(T)1166 4387 y Ff(\027)s Fm(+1)1125 4451 y Fn(\027)t
Fo(0)1286 4426 y Fv(\))p Fq(j)26 b Fv(=)f Fq(j)p Fp(Q)1565
4388 y Fo(0)1565 4448 y(00)1640 4426 y Fq(j)g(\024)g(j)p
Fp(Q)1883 4440 y Fo(00)1958 4426 y Fq(j)1983 4441 y Fn(r)2015
4450 y Fm(0)2050 4441 y Fn(;s)2103 4450 y Fm(0)2136 4441
y Fn(;h)2197 4450 y Fm(0)2235 4426 y Fp(e)2277 4388 y
Fx(\000j)p Fn(k)r Fx(j)p Fn(r)2443 4397 y Fm(0)2506 4426
y Fq(\024)g(j)p Fp(Q)2699 4440 y Fo(0)2739 4426 y Fq(j)2764
4441 y Fn(r)2796 4450 y Fm(0)2830 4441 y Fn(;s)2883 4450
y Fm(0)2917 4441 y Fn(;h)2978 4450 y Fm(0)3041 4426 y
Fp(<)g(\015)5 b(s)25 b(<)3363 4364 y(h)p 3363 4405 53
4 v 3366 4488 a Fv(4)165 4665 y(pro)m(vided)e(that)i(0)h
Fp(<)e(s)h(<)1081 4629 y Fn(h)p 1063 4644 76 4 v 1063
4696 a Fo(4)p Fn(\015)1149 4665 y Fv(.)38 b(Th)m(us,)25
b(for)e(the)h(mapping)g Fp(a)2161 4679 y Fn(\027)2229
4665 y Fq(7!)h Fp(a)2393 4679 y Fn(\027)t Fo(+1)2552
4665 y Fv(=)g Fp(a)2696 4679 y Fn(\027)2746 4665 y Fq(\000)7
b Fp(\033)2876 4679 y Fn(\027)2919 4665 y Fv(\()p Fp(a)3002
4679 y Fn(\027)3046 4665 y Fv(\),)26 b(b)m(y)d(Lemma)h(A.3)165
4778 y(of)30 b(App)s(endix)f(A)i(in)f([15)q(],)h(there)f(exists)h(a)g
(real)g(analytic)h(in)m(v)m(erse)f(mapping)1571 4977
y(id)20 b(+)g Fp(\036)25 b Fv(:)h Fp(a)1936 4991 y Fn(\027)t
Fo(+1)2095 4977 y Fq(7!)f Fp(a)2259 4991 y Fn(\027)165
5175 y Fv(suc)m(h)30 b(that)h(\(id)20 b(+)g Fp(\036)p
Fv(\)\()p Fp(O)982 5190 y Fn(h)1023 5199 y Ff(\027)s
Fm(+1)1144 5175 y Fv(\))25 b Fq(\032)g Fp(O)1369 5190
y Fn(h)1410 5198 y Ff(\027)1483 5175 y Fv(with)30 b(the)h(estimates)
1629 5425 y Fq(j)p Fp(\036)p Fq(j)p Fp(;)1784 5364 y(h)p
1784 5404 53 4 v 1787 5488 a Fv(4)1846 5425 y Fq(j)p
Fp(D)s(\036)p Fq(j)26 b(\024)f Fp(\015)5 b(s)1891 5691
y Fv(10)p eop end
%%Page: 11 11
TeXDict begin 11 10 bop 165 337 a Fv(on)30 b Fp(O)360
355 y Fn(h=)p Fo(4)476 337 y Fv(.)41 b(W)-8 b(e)31 b(therefore)g(ha)m
(v)m(e)g(obtained)g(a)g(transformation)2383 310 y Fg(e)2359
337 y Fq(F)2424 351 y Fn(\027)2492 337 y Fv(=)25 b(\()p
Fp(S)2679 351 y Fn(\027)2723 337 y Fp(;)15 b Fv(id)20
b(+)g Fp(\036)p Fv(\))31 b(suc)m(h)f(that)1178 531 y
Fg(e)1154 558 y Fq(F)1219 572 y Fn(\027)1262 558 y Fv(\()p
Fp(D)1372 572 y Fn(r)1404 581 y Ff(\027)s Fm(+1)1520
572 y Fn(;s)1573 581 y Ff(\027)s Fm(+1)1712 558 y Fq(\002)20
b Fp(O)1872 573 y Fn(h)1913 582 y Ff(\027)s Fm(+1)2033
558 y Fv(\))26 b Fq(\032)f Fp(D)2265 572 y Fn(r)2297
580 y Ff(\027)2335 572 y Fn(;s)2388 580 y Ff(\027)2450
558 y Fq(\002)20 b Fp(O)2610 573 y Fn(h)2651 581 y Ff(\027)2694
558 y Fp(:)757 b Fv(\(2.22\))165 762 y(No)m(w,)31 b(w)m(e)g(estimate)h
(the)f(functions)f Fp(R)1513 776 y Fn(\027)t Fo(+1)1676
762 y Fv(and)g Fp(Q)1925 776 y Fn(\027)t Fo(+1)2058 762
y Fv(.)41 b(F)-8 b(rom)31 b(\(2.14\),)i(\(2.15\))f(and)e(\(2.16\),)j(w)
m(e)e(ha)m(v)m(e)894 966 y Fp(R)963 980 y Fn(\027)t Fo(+1)1121
966 y Fv(=)25 b(\(1)c(+)f Fp(f)1454 980 y Fn(\027)t Fo(1)1532
966 y Fv(\))1567 929 y Fx(\000)p Fo(1)1677 966 y Fv([)p
Fp(M)1790 980 y Fo(1)1850 966 y Fv(+)g Fp(M)2029 980
y Fo(2)2089 966 y Fv(+)g(\()p Fp(M)2303 980 y Fo(3)2363
966 y Fv(+)g Fp(M)2542 980 y Fo(4)2582 966 y Fv(\))15
b Fp(I)2672 980 y Fn(\027)2735 966 y Fv(+)20 b Fp(M)2914
980 y Fo(5)2954 966 y Fv(])497 b(\(2.23\))165 1170 y(and)1215
1320 y Fp(Q)1287 1334 y Fn(\027)t Fo(+1)1445 1320 y Fv(=)1541
1201 y Fg(\022)1603 1320 y Fv(1)20 b(+)1805 1258 y Fp(@)5
b(g)1901 1272 y Fn(\027)t Fo(0)p 1769 1299 247 4 v 1769
1382 a Fp(@)g(')1881 1396 y Fn(\027)t Fo(+1)2025 1201
y Fg(\023)2086 1222 y Fx(\000)p Fo(1)2196 1320 y Fv(\()p
Fp(M)2319 1334 y Fo(6)2379 1320 y Fv(+)20 b Fp(M)2558
1334 y Fo(7)2597 1320 y Fv(\))p Fp(;)819 b Fv(\(2.24\))165
1528 y(where)293 1732 y Fp(M)381 1746 y Fo(1)504 1732
y Fv(=)83 b Fp(R)727 1746 y Fn(\027)t Fo(0)805 1732 y
Fv(\()p Fp(')899 1746 y Fn(\027)t Fo(+1)1053 1732 y Fv(+)20
b Fp(g)1187 1746 y Fn(\027)t Fo(0)1266 1732 y Fp(;)15
b(t;)g(a)1427 1746 y Fn(\027)t Fo(+1)1581 1732 y Fv(+)20
b Fp(\033)1724 1746 y Fn(\027)1767 1732 y Fv(\))h Fq(\000)f
Fp(R)1983 1746 y Fn(\027)t Fo(0)2061 1732 y Fv(\()p Fp(')2155
1746 y Fn(\027)t Fo(+1)2290 1732 y Fp(;)15 b(t;)g(a)2451
1746 y Fn(\027)t Fo(+1)2605 1732 y Fv(+)20 b Fp(\033)2748
1746 y Fn(\027)2791 1732 y Fv(\))p Fp(;)293 1881 y(M)381
1895 y Fo(2)504 1881 y Fv(=)83 b Fp(R)727 1895 y Fn(\027)t
Fo(0)805 1881 y Fv(\()p Fp(')899 1895 y Fn(\027)t Fo(+1)1033
1881 y Fp(;)15 b(t;)g(a)1194 1895 y Fn(\027)t Fo(+1)1349
1881 y Fv(+)k Fp(\033)1491 1895 y Fn(\027)1535 1881 y
Fv(\))h Fq(\000)g Fp(R)1751 1834 y Fn(T)1792 1843 y Ff(\027)s
Fm(+1)1750 1906 y Fn(\027)t Fo(0)1912 1881 y Fv(\()p
Fp(')2006 1895 y Fn(\027)t Fo(+1)2140 1881 y Fp(;)15
b(t;)g(a)2301 1895 y Fn(\027)t Fo(+1)2455 1881 y Fv(+)20
b Fp(\033)2598 1895 y Fn(\027)2641 1881 y Fv(\))p Fp(;)293
2019 y(M)381 2033 y Fo(3)504 2019 y Fv(=)83 b Fp(R)727
2033 y Fn(\027)t Fo(1)805 2019 y Fv(\()p Fp(')899 2033
y Fn(\027)t Fo(+1)1053 2019 y Fv(+)20 b Fp(g)1187 2033
y Fn(\027)t Fo(0)1266 2019 y Fp(;)15 b(t;)g(a)1427 2033
y Fn(\027)t Fo(+1)1581 2019 y Fv(+)20 b Fp(\033)1724
2033 y Fn(\027)1767 2019 y Fv(\))h Fq(\000)f Fp(R)1983
2033 y Fn(\027)t Fo(1)2061 2019 y Fv(\()p Fp(')2155 2033
y Fn(\027)t Fo(+1)2290 2019 y Fp(;)15 b(t;)g(a)2451 2033
y Fn(\027)t Fo(+1)2605 2019 y Fv(+)20 b Fp(\033)2748
2033 y Fn(\027)2791 2019 y Fv(\))p Fp(;)293 2168 y(M)381
2182 y Fo(4)504 2168 y Fv(=)83 b Fp(R)727 2182 y Fn(\027)t
Fo(1)805 2168 y Fv(\()p Fp(')899 2182 y Fn(\027)t Fo(+1)1033
2168 y Fp(;)15 b(t;)g(a)1194 2182 y Fn(\027)t Fo(+1)1349
2168 y Fv(+)k Fp(\033)1491 2182 y Fn(\027)1535 2168 y
Fv(\))h Fq(\000)g Fp(R)1751 2120 y Fn(T)1792 2129 y Ff(\027)s
Fm(+1)1750 2193 y Fn(\027)t Fo(1)1912 2168 y Fv(\()p
Fp(')2006 2182 y Fn(\027)t Fo(+1)2140 2168 y Fp(;)15
b(t;)g(a)2301 2182 y Fn(\027)t Fo(+1)2455 2168 y Fv(+)20
b Fp(\033)2598 2182 y Fn(\027)2641 2168 y Fv(\))p Fp(;)293
2350 y(M)381 2364 y Fo(5)504 2350 y Fv(=)83 b Fp(R)728
2303 y Fn(T)769 2312 y Ff(\027)s Fm(+1)727 2375 y Fn(\027)t
Fo(1)888 2350 y Fv(\()p Fp(')982 2364 y Fn(\027)t Fo(+1)1116
2350 y Fp(;)15 b(t;)g(a)1277 2364 y Fn(\027)t Fo(+1)1432
2350 y Fv(+)k Fp(\033)1574 2364 y Fn(\027)1618 2350 y
Fv(\))c(\()p Fp(f)1748 2364 y Fn(\027)t Fo(0)1847 2350
y Fv(+)k Fp(f)1982 2364 y Fn(\027)t Fo(1)2060 2350 y
Fp(I)2100 2364 y Fn(\027)t Fo(+1)2234 2350 y Fv(\))h
Fq(\000)2380 2231 y Fg(\022)2486 2289 y Fp(@)5 b(f)2584
2303 y Fn(\027)t Fo(0)p 2451 2329 V 2451 2413 a Fp(@)g(')2563
2427 y Fn(\027)t Fo(+1)2728 2350 y Fv(+)2863 2289 y Fp(@)g(f)2961
2303 y Fn(\027)t Fo(1)p 2829 2329 V 2829 2413 a Fp(@)g(')2941
2427 y Fn(\027)t Fo(+1)3085 2350 y Fp(I)3125 2364 y Fn(\027)t
Fo(+1)3258 2231 y Fg(\023)3334 2350 y Fp(Q)3406 2364
y Fn(\027)t Fo(+1)3539 2350 y Fp(;)293 2535 y(M)381 2549
y Fo(6)504 2535 y Fv(=)83 b Fp(Q)730 2549 y Fn(\027)t
Fo(0)808 2535 y Fv(\()p Fp(')902 2549 y Fn(\027)t Fo(+1)1056
2535 y Fv(+)20 b Fp(g)1190 2549 y Fn(\027)t Fo(0)1269
2535 y Fp(;)15 b(t;)g(a)1430 2549 y Fn(\027)t Fo(+1)1584
2535 y Fv(+)20 b Fp(\033)1727 2549 y Fn(\027)1770 2535
y Fv(\))h Fq(\000)f Fp(Q)1989 2549 y Fn(\027)t Fo(0)2067
2535 y Fv(\()p Fp(')2161 2549 y Fn(\027)t Fo(+1)2295
2535 y Fp(;)15 b(t;)g(a)2456 2549 y Fn(\027)t Fo(+1)2611
2535 y Fv(+)k Fp(\033)2753 2549 y Fn(\027)2797 2535 y
Fv(\))p Fp(;)293 2683 y(M)381 2697 y Fo(7)504 2683 y
Fv(=)83 b Fp(Q)730 2697 y Fn(\027)t Fo(0)808 2683 y Fv(\()p
Fp(')902 2697 y Fn(\027)t Fo(+1)1036 2683 y Fp(;)15 b(t;)g(a)1197
2697 y Fn(\027)t Fo(+1)1351 2683 y Fv(+)20 b Fp(\033)1494
2697 y Fn(\027)1537 2683 y Fv(\))h Fq(\000)f Fp(Q)1756
2636 y Fn(T)1797 2645 y Ff(\027)s Fm(+1)1756 2708 y Fn(\027)t
Fo(0)1916 2683 y Fv(\()p Fp(')2010 2697 y Fn(\027)t Fo(+1)2145
2683 y Fp(;)15 b(t;)g(a)2306 2697 y Fn(\027)t Fo(+1)2460
2683 y Fv(+)20 b Fp(\033)2603 2697 y Fn(\027)2646 2683
y Fv(\))p Fp(:)165 2888 y Fv(First,)31 b(w)m(e)g(ha)m(v)m(e)g(the)g
(follo)m(wing)h(estimates)895 3130 y Fq(j)966 3068 y
Fp(@)5 b(g)1062 3082 y Fn(\027)t Fo(0)p 930 3109 V 930
3192 a Fp(@)g(')1042 3206 y Fn(\027)t Fo(+1)1186 3130
y Fq(j)84 b(\024)1620 3068 y Fv(1)p 1458 3109 370 4 v
1458 3192 a Fp(r)1499 3206 y Fn(\027)1563 3192 y Fq(\000)20
b Fp(r)1695 3206 y Fn(\027)t Fo(+1)1838 3130 y Fq(j)p
Fp(g)1906 3144 y Fn(\027)t Fo(0)1985 3130 y Fq(j)2010
3145 y Fn(r)2042 3153 y Ff(\027)2081 3145 y Fn(;s)2134
3153 y Ff(\027)2171 3145 y Fn(;h)2232 3153 y Ff(\027)2299
3130 y Fq(\024)2405 3068 y Fp(T)2458 3082 y Fn(\027)p
2405 3109 97 4 v 2431 3192 a Fv(2)2532 3130 y Fq(\001)2624
3068 y Fp(c)2663 3082 y Fo(1)2702 3068 y Fp(s)p 2587
3109 195 4 v 2587 3192 a(T)2640 3206 y Fn(\027)2684 3192
y Fp(\026)2739 3166 y Fn(\034)2817 3130 y Fq(\024)2923
3068 y Fv(1)p 2923 3109 46 4 v 2923 3192 a(4)165 3391
y(pro)m(vided)30 b(that)h(0)26 b Fp(<)e(s)h(<)1091 3355
y Fo(2)p 1076 3370 66 4 v 1076 3422 a Fn(c)1107 3431
y Fm(2)1151 3391 y Fv(,)31 b(and)659 3656 y Fq(j)p Fp(M)772
3670 y Fo(6)812 3656 y Fq(j)83 b(\024)1074 3533 y Fg(\014)1074
3583 y(\014)1074 3633 y(\014)1074 3683 y(\014)1133 3594
y Fp(@)5 b(Q)1258 3608 y Fn(\027)t Fo(0)p 1112 3635 247
4 v 1112 3718 a Fp(@)g(')1224 3732 y Fn(\027)t Fo(+1)1368
3533 y Fg(\014)1368 3583 y(\014)1368 3633 y(\014)1368
3683 y(\014)1411 3656 y Fq(j)p Fp(g)1479 3670 y Fn(\027)t
Fo(0)1558 3656 y Fq(j)25 b(\024)1876 3594 y Fv(1)p 1714
3635 370 4 v 1714 3718 a Fp(r)1755 3732 y Fn(\027)1819
3718 y Fq(\000)20 b Fp(r)1951 3732 y Fn(\027)t Fo(+1)2094
3656 y Fq(j)p Fp(Q)2191 3670 y Fn(\027)t Fo(0)2269 3656
y Fq(j)2294 3671 y Fn(r)2326 3679 y Ff(\027)2365 3671
y Fn(;s)2418 3679 y Ff(\027)2456 3671 y Fn(;h)2517 3679
y Ff(\027)2559 3656 y Fq(j)p Fp(g)2627 3670 y Fn(\027)t
Fo(0)2706 3656 y Fq(j)920 3895 y(\024)1246 3834 y Fv(1)p
1084 3874 V 1084 3958 a Fp(r)1125 3972 y Fn(\027)1189
3958 y Fq(\000)f Fp(r)1320 3972 y Fn(\027)t Fo(+1)1464
3895 y Fq(j)p Fp(Q)1561 3909 y Fn(\027)1604 3895 y Fq(j)1629
3910 y Fn(r)1661 3918 y Ff(\027)1700 3910 y Fn(;s)1753
3918 y Ff(\027)1790 3910 y Fn(;h)1851 3918 y Ff(\027)1893
3895 y Fq(j)p Fp(g)1961 3909 y Fn(\027)t Fo(0)2040 3895
y Fq(j)26 b(\024)2197 3834 y Fp(T)2250 3848 y Fn(\027)p
2197 3874 97 4 v 2222 3958 a Fv(2)2303 3895 y Fp(\015)5
b(s)2398 3909 y Fn(\027)2487 3834 y Fp(c)2526 3848 y
Fo(1)2566 3834 y Fp(s)p 2451 3874 195 4 v 2451 3958 a(T)2504
3972 y Fn(\027)2547 3958 y Fp(\026)2602 3931 y Fn(\034)2680
3895 y Fv(=)25 b Fp(c)2815 3909 y Fo(1)2855 3895 y Fp(\015)5
b(ss)2993 3909 y Fn(\027)3036 3895 y Fp(\026)3091 3858
y Fx(\000)p Fn(\034)3189 3895 y Fp(:)165 4172 y Fv(Note)32
b(that)f Fp(T)635 4186 y Fn(\027)704 4172 y Fq(!)26 b(1)31
b Fv(as)g Fp(\026)25 b Fq(!)h Fv(0,)32 b(w)m(e)f(can)g(c)m(ho)s(ose)h
Fp(\026)1999 4139 y Fx(\003)2064 4172 y Fp(>)25 b Fv(0)31
b(so)g(small)g(that)h Fp(T)2850 4131 y Fn(N)2906 4140
y Fm(1)2940 4131 y Fo(+)p Fn(N)3051 4140 y Fm(2)2837
4196 y Fn(\027)t Fo(+1)3090 4172 y Fp(e)3132 4136 y Fx(\000)3197
4099 y Ff(r)3226 4114 y Fm(0)p 3197 4121 64 4 v 3213
4162 a(2)3270 4136 y Fn(T)3311 4145 y Ff(\027)s Fm(+1)3457
4172 y Fp(<)26 b(s)k Fv(as)165 4285 y(0)c Fp(<)f(\026)g(<)g(\026)563
4252 y Fx(\003)602 4285 y Fv(.)40 b(Th)m(us,)30 b(from)g(Lemma)g(A.2)i
(in)e([15)q(])g(w)m(e)h(ha)m(v)m(e)395 4502 y Fq(j)p
Fp(M)508 4516 y Fo(7)547 4502 y Fq(j)84 b(\024)906 4422
y Fg(X)809 4610 y Fx(j)p Fn(k)r Fx(j)p Fn(>T)10 b(\027)t
Fo(+1)1137 4502 y Fq(j)p Fp(Q)1234 4465 y Fo(0)1234 4525
y Fn(k)1271 4534 y Fm(1)1306 4525 y Fn(k)1343 4534 y
Fm(2)1381 4502 y Fp(e)1423 4465 y Fn(i)p Fx(h)p Fn(k)1511
4474 y Fm(1)1546 4465 y Fn(;)p Fo(\012)1617 4474 y Fm(1)1652
4465 y Fx(i)p Fn(t)p Fo(+)p Fn(i)p Fx(h)p Fn(k)1847 4474
y Fm(2)1882 4465 y Fn(;)p Fo(\012)1953 4474 y Fm(2)1987
4465 y Fx(i)p Fn(')2060 4474 y Ff(\027)s Fm(+1)2180 4502
y Fq(j)26 b(\024)f Fp(cT)2432 4462 y Fn(N)2488 4471 y
Fm(1)2523 4462 y Fo(+)p Fn(N)2634 4471 y Fm(2)2419 4527
y Fn(\027)t Fo(+1)2672 4502 y Fp(e)2714 4465 y Fx(\000)2779
4428 y Ff(r)2808 4443 y Fm(0)p 2779 4450 V 2796 4491
a(2)2853 4465 y Fn(T)2894 4474 y Ff(\027)s Fm(+1)3014
4502 y Fq(j)p Fp(Q)3111 4516 y Fn(\027)t Fo(0)3189 4502
y Fq(j)3214 4517 y Fn(r)3246 4525 y Ff(\027)3285 4517
y Fn(;s)3338 4525 y Ff(\027)3376 4517 y Fn(;h)3437 4525
y Ff(\027)656 4763 y Fq(\024)82 b Fp(cT)914 4723 y Fn(N)970
4732 y Fm(1)1005 4723 y Fo(+)p Fn(N)1116 4732 y Fm(2)901
4788 y Fn(\027)t Fo(+1)1155 4763 y Fp(e)1197 4726 y Fx(\000)1262
4689 y Ff(r)1291 4704 y Fm(0)p 1262 4711 V 1278 4752
a(2)1335 4726 y Fn(T)1376 4735 y Ff(\027)s Fm(+1)1496
4763 y Fq(j)p Fp(Q)1593 4777 y Fn(\027)1636 4763 y Fq(j)1661
4778 y Fn(r)1693 4786 y Ff(\027)1732 4778 y Fn(;s)1785
4786 y Ff(\027)1823 4778 y Fn(;h)1884 4786 y Ff(\027)1951
4763 y Fq(\024)25 b Fp(c\015)5 b(ss)2224 4777 y Fn(\027)2267
4763 y Fp(;)165 4968 y Fv(where)30 b Fp(c)g Fv(only)h(dep)s(ends)d(on)j
Fp(N)1248 4982 y Fo(1)1307 4968 y Fv(+)20 b Fp(N)1471
4982 y Fo(2)1511 4968 y Fv(.)40 b(It)31 b(follo)m(ws)g(that)366
5205 y Fq(j)p Fp(Q)463 5219 y Fn(\027)t Fo(+1)596 5205
y Fq(j)621 5220 y Fn(r)653 5229 y Ff(\027)s Fm(+1)769
5220 y Fn(;s)822 5229 y Ff(\027)s Fm(+1)936 5220 y Fn(;h)997
5229 y Ff(\027)s Fm(+1)1199 5205 y Fq(\024)1555 5144
y Fv(1)p 1363 5184 430 4 v 1363 5281 a(1)21 b Fq(\000)f(j)1584
5240 y Fn(@)t(g)1659 5249 y Ff(\027)s Fm(0)p 1555 5260
203 4 v 1555 5312 a Fn(@)t(')1642 5321 y Ff(\027)s Fm(+1)1767
5281 y Fq(j)1803 5205 y Fv(\()p Fq(j)p Fp(M)1951 5219
y Fo(6)1991 5205 y Fq(j)g Fv(+)g Fq(j)p Fp(M)2240 5219
y Fo(7)2280 5205 y Fq(j)p Fv(\))26 b Fq(\024)2555 5144
y Fv(1)p 2472 5184 212 4 v 2472 5273 a(1)21 b Fq(\000)2638
5237 y Fo(1)p 2638 5252 36 4 v 2638 5304 a(4)2694 5205
y Fv(\()p Fp(c)2768 5219 y Fo(1)2808 5205 y Fp(\015)5
b(ss)2946 5219 y Fn(\027)2988 5205 y Fp(\026)3043 5168
y Fx(\000)p Fn(\034)3161 5205 y Fv(+)20 b Fp(c\015)5
b(ss)3429 5219 y Fn(\027)3472 5205 y Fv(\))1199 5410
y Fp(<)83 b(\015)5 b(s)1448 5424 y Fn(\027)t Fo(+1)1891
5691 y Fv(11)p eop end
%%Page: 12 12
TeXDict begin 12 11 bop 165 337 a Fv(pro)m(vided)30 b(that)h(0)26
b Fp(<)e(s)h(<)1110 296 y Fo(3)p Fn(\026)1187 273 y Ff(\024)p
1076 316 186 4 v 1076 368 a Fn(c)1107 377 y Fm(2)1141
368 y Fo(+4)p Fn(c)1272 337 y Fv(.)41 b(Moreo)m(v)m(er,)33
b(w)m(e)d(also)i(ha)m(v)m(e)f(the)g(estimates)165 625
y Fq(j)p Fp(M)278 639 y Fo(5)318 625 y Fq(j)83 b(\024)580
453 y Fg(\014)580 503 y(\014)580 553 y(\014)580 602 y(\014)580
652 y(\014)580 702 y(\014)704 544 y(X)607 733 y Fx(j)p
Fn(k)r Fx(j\024)p Fn(T)10 b(\027)t Fo(+1)935 625 y Fp(R)1005
588 y Fo(1)1004 648 y Fn(k)1041 657 y Fm(1)1076 648 y
Fn(k)1113 657 y Fm(2)1151 625 y Fp(e)1193 588 y Fn(i)p
Fx(h)p Fn(k)1281 597 y Fm(1)1316 588 y Fn(;)p Fo(\012)1387
597 y Fm(1)1421 588 y Fx(i)p Fn(t)p Fo(+)p Fn(i)p Fx(h)p
Fn(k)1616 597 y Fm(2)1652 588 y Fn(;)p Fo(\012)1723 597
y Fm(2)1757 588 y Fx(i)p Fn(')1830 597 y Ff(\027)s Fm(+1)1950
453 y Fg(\014)1950 503 y(\014)1950 553 y(\014)1950 602
y(\014)1950 652 y(\014)1950 702 y(\014)1993 625 y Fq(j)p
Fp(f)2063 639 y Fn(\027)t Fo(0)2162 625 y Fv(+)19 b Fp(f)2297
639 y Fn(\027)t Fo(1)2375 625 y Fp(I)2415 639 y Fn(\027)t
Fo(+1)2549 625 y Fq(j)h Fv(+)2685 503 y Fg(\014)2685
553 y(\014)2685 602 y(\014)2685 652 y(\014)2713 506 y(\022)2819
564 y Fp(@)5 b(f)2917 578 y Fn(\027)t Fo(0)p 2784 604
247 4 v 2784 688 a Fp(@)g(')2896 702 y Fn(\027)t Fo(+1)3060
625 y Fv(+)3196 564 y Fp(@)g(f)3294 578 y Fn(\027)t Fo(1)p
3161 604 V 3161 688 a Fp(@)g(')3273 702 y Fn(\027)t Fo(+1)3417
625 y Fp(I)3457 639 y Fn(\027)t Fo(+1)3590 506 y Fg(\023)3667
625 y Fp(Q)3739 639 y Fn(\027)t Fo(+1)3872 503 y Fg(\014)3872
553 y(\014)3872 602 y(\014)3872 652 y(\014)426 963 y
Fq(\024)580 794 y Fg(0)580 943 y(@)749 882 y(X)652 1070
y Fx(j)p Fn(k)r Fx(j\024)p Fn(T)10 b(\027)t Fo(+1)1010
901 y Fv(1)p 990 942 86 4 v 990 1025 a Fp(s)1033 1039
y Fn(\027)1086 963 y Fq(j)p Fp(R)1180 977 y Fn(\027)1223
963 y Fq(j)1248 978 y Fn(r)1280 986 y Ff(\027)1319 978
y Fn(;s)1372 986 y Ff(\027)1410 978 y Fn(;h)1471 986
y Ff(\027)1513 963 y Fp(e)1555 925 y Fx(\000j)p Fn(k)r
Fx(j)p Fo(\()p Fn(r)1748 933 y Ff(\027)1785 925 y Fx(\000)p
Fn(r)1872 934 y Ff(\027)s Fm(+1)1988 925 y Fo(\))2019
794 y Fg(1)2019 943 y(A)2107 963 y Fq(j)p Fp(f)2177 977
y Fn(\027)t Fo(0)2276 963 y Fv(+)19 b Fp(f)2411 977 y
Fn(\027)t Fo(1)2489 963 y Fp(I)2529 977 y Fn(\027)t Fo(+1)2663
963 y Fq(j)h Fv(+)2971 901 y(1)p 2809 942 370 4 v 2809
1025 a Fp(r)2850 1039 y Fn(\027)2913 1025 y Fq(\000)g
Fp(r)3045 1039 y Fn(\027)t Fo(+1)3189 963 y Fq(j)p Fp(f)3259
977 y Fn(\027)t Fo(0)3357 963 y Fv(+)g Fp(f)3493 977
y Fn(\027)t Fo(1)3571 963 y Fp(I)3611 977 y Fn(\027)t
Fo(+1)3744 963 y Fq(jj)p Fp(Q)3866 977 y Fn(\027)t Fo(+1)4000
963 y Fq(j)426 1280 y(\024)622 1219 y Fp(c)661 1233 y
Fo(1)701 1219 y Fp(\015)5 b(s)796 1233 y Fn(\027)p 590
1259 283 4 v 590 1345 a Fp(\026)645 1319 y Fn(\034)j
Fo(\()p Fn(\027)t Fo(+1\))902 1280 y Fq(\001)957 1219
y Fp(c)996 1233 y Fo(1)1036 1219 y Fp(s)1079 1233 y Fn(\027)1122
1219 y Fv(\()p Fp(s)1200 1233 y Fn(\027)1263 1219 y Fv(+)20
b Fp(s)1397 1233 y Fn(\027)t Fo(+1)1530 1219 y Fv(\))p
957 1259 609 4 v 1120 1345 a Fp(\026)1175 1319 y Fn(\034)8
b Fo(\()p Fn(\027)t Fo(+1\))1596 1280 y Fv(+)1696 1214
y Fp(\015)d(s)1791 1228 y Fn(\027)t Fo(+1)1925 1214 y
Fp(s)1968 1228 y Fn(\027)2010 1214 y Fv(\()p Fp(s)2088
1228 y Fn(\027)2152 1214 y Fv(+)20 b Fp(s)2286 1228 y
Fn(\027)t Fo(+1)2419 1214 y Fv(\)\()p Fp(N)2562 1228
y Fo(1)2622 1214 y Fv(+)g Fp(N)2786 1228 y Fo(2)2825
1214 y Fv(\)!4)2930 1181 y Fn(N)2986 1190 y Fm(1)3022
1181 y Fo(+)p Fn(N)3133 1190 y Fm(2)3172 1214 y Fp(T)3238
1174 y Fn(N)3294 1183 y Fm(1)3328 1174 y Fo(+)p Fn(N)3439
1183 y Fm(2)3474 1174 y Fo(+1)3225 1239 y Fn(\027)t Fo(+1)p
1696 1259 1872 4 v 2375 1343 a Fp(T)2441 1311 y Fn($)2428
1367 y(\027)t Fo(+1)2561 1343 y Fv(\011\()p Fp(T)2720
1357 y Fn(\027)t Fo(+1)2854 1343 y Fv(\))426 1545 y Fq(\024)590
1483 y Fp(\015)5 b(c)681 1450 y Fo(2)681 1506 y(1)721
1483 y Fp(s)764 1450 y Fo(2)764 1506 y Fn(\027)806 1483
y Fv(\()p Fp(s)884 1497 y Fn(\027)948 1483 y Fv(+)20
b Fp(s)1082 1497 y Fn(\027)t Fo(+1)1215 1483 y Fv(\))p
590 1524 661 4 v 761 1610 a Fp(\026)816 1583 y Fo(2)p
Fn(\034)8 b Fo(\()p Fn(\027)t Fo(+1\))1280 1545 y Fv(+)1381
1483 y Fp(\015)d(c)1472 1497 y Fo(1)1512 1483 y Fp(s)1555
1497 y Fn(\027)t Fo(+1)1688 1483 y Fp(s)1731 1497 y Fn(\027)1774
1483 y Fv(\()p Fp(s)1852 1497 y Fn(\027)1915 1483 y Fv(+)20
b Fp(s)2049 1497 y Fn(\027)t Fo(+1)2182 1483 y Fv(\))p
1381 1524 837 4 v 1658 1610 a Fp(\026)1713 1583 y Fn(\034)8
b Fo(\()p Fn(\027)t Fo(+1\))2227 1545 y Fp(;)165 1767
y Fv(and)347 1967 y Fq(j)p Fp(M)460 1981 y Fo(1)500 1967
y Fq(j)83 b(\024)762 1845 y Fg(\014)762 1894 y(\014)762
1944 y(\014)762 1994 y(\014)822 1905 y Fp(@)5 b(R)944
1919 y Fn(\027)t Fo(0)p 800 1946 247 4 v 800 2029 a Fp(@)g(')912
2043 y Fn(\027)t Fo(+1)1056 1845 y Fg(\014)1056 1894
y(\014)1056 1944 y(\014)1056 1994 y(\014)1099 1967 y
Fq(j)p Fp(g)1167 1981 y Fn(\027)t Fo(0)1246 1967 y Fq(j)25
b(\024)1564 1905 y Fv(1)p 1402 1946 370 4 v 1402 2029
a Fp(r)1443 2043 y Fn(\027)1506 2029 y Fq(\000)20 b Fp(r)1638
2043 y Fn(\027)t Fo(+1)1782 1967 y Fq(j)p Fp(R)1876 1981
y Fn(\027)t Fo(0)1954 1967 y Fq(j)1979 1982 y Fn(r)2011
1990 y Ff(\027)2050 1982 y Fn(;s)2103 1990 y Ff(\027)2141
1982 y Fn(;h)2202 1990 y Ff(\027)2244 1967 y Fq(j)p Fp(g)2312
1981 y Fn(\027)t Fo(0)2391 1967 y Fq(j)25 b(\024)2709
1905 y Fv(1)p 2547 1946 V 2547 2029 a Fp(r)2588 2043
y Fn(\027)2652 2029 y Fq(\000)20 b Fp(r)2784 2043 y Fn(\027)t
Fo(+1)2927 1967 y Fq(j)p Fp(R)3021 1981 y Fn(\027)3064
1967 y Fq(j)3089 1982 y Fn(r)3121 1990 y Ff(\027)3160
1982 y Fn(;s)3213 1990 y Ff(\027)3251 1982 y Fn(;h)3312
1990 y Ff(\027)3354 1967 y Fq(j)p Fp(g)3422 1981 y Fn(\027)t
Fo(0)3501 1967 y Fq(j)608 2207 y(\024)772 2145 y Fp(T)825
2159 y Fn(\027)p 772 2186 97 4 v 797 2269 a Fv(2)878
2207 y Fp(\015)5 b(s)973 2169 y Fo(2)973 2229 y Fn(\027)1062
2145 y Fp(c)1101 2159 y Fo(1)1141 2145 y Fp(s)p 1026
2186 195 4 v 1026 2269 a(T)1079 2283 y Fn(\027)1122 2269
y Fp(\026)1177 2243 y Fn(\034)1256 2207 y Fv(=)24 b Fp(c)1390
2221 y Fo(1)1430 2207 y Fp(\015)5 b(ss)1568 2169 y Fo(2)1568
2229 y Fn(\027)1611 2207 y Fp(\026)1666 2169 y Fx(\000)p
Fn(\034)1764 2207 y Fp(;)347 2482 y Fq(j)p Fp(M)460 2496
y Fo(2)500 2482 y Fq(j)83 b(\024)858 2401 y Fg(X)762
2590 y Fx(j)p Fn(k)r Fx(j)p Fn(>T)10 b(\027)t Fo(+1)1090
2482 y Fq(j)p Fp(R)1185 2445 y Fo(0)1184 2505 y Fn(k)1221
2514 y Fm(1)1255 2505 y Fn(k)1292 2514 y Fm(2)1331 2482
y Fp(e)1373 2445 y Fn(i)p Fx(h)p Fn(k)1461 2454 y Fm(1)1496
2445 y Fn(;)p Fo(\012)1567 2454 y Fm(1)1601 2445 y Fx(i)p
Fn(t)p Fo(+)p Fn(i)p Fx(h)p Fn(k)1796 2454 y Fm(2)1832
2445 y Fn(;)p Fo(\012)1903 2454 y Fm(2)1937 2445 y Fx(i)p
Fn(')2010 2454 y Ff(\027)s Fm(+1)2130 2482 y Fq(j)26
b(\024)f Fp(cT)2382 2442 y Fn(N)2438 2451 y Fm(1)2472
2442 y Fo(+)p Fn(N)2583 2451 y Fm(2)2369 2507 y Fn(\027)t
Fo(+1)2622 2482 y Fp(e)2664 2445 y Fx(\000)2729 2408
y Ff(r)2758 2423 y Fm(0)p 2729 2430 64 4 v 2746 2471
a(2)2803 2445 y Fn(T)2844 2454 y Ff(\027)s Fm(+1)2963
2482 y Fq(j)p Fp(R)3057 2496 y Fn(\027)t Fo(0)3136 2482
y Fq(j)3161 2497 y Fn(r)3193 2505 y Ff(\027)3232 2497
y Fn(;s)3285 2505 y Ff(\027)3322 2497 y Fn(;h)3383 2505
y Ff(\027)608 2743 y Fq(\024)83 b Fp(cT)867 2703 y Fn(N)923
2712 y Fm(1)958 2703 y Fo(+)p Fn(N)1069 2712 y Fm(2)854
2768 y Fn(\027)t Fo(+1)1107 2743 y Fp(e)1149 2706 y Fx(\000)1214
2669 y Ff(r)1243 2684 y Fm(0)p 1214 2691 V 1231 2732
a(2)1288 2706 y Fn(T)1329 2715 y Ff(\027)s Fm(+1)1449
2743 y Fq(j)p Fp(R)1543 2757 y Fn(\027)1586 2743 y Fq(j)1611
2758 y Fn(r)1643 2766 y Ff(\027)1682 2758 y Fn(;s)1735
2766 y Ff(\027)1773 2758 y Fn(;h)1834 2766 y Ff(\027)1901
2743 y Fq(\024)25 b Fp(c\015)5 b(ss)2174 2706 y Fo(2)2174
2766 y Fn(\027)2217 2743 y Fp(;)347 3039 y Fq(j)p Fp(M)460
3053 y Fo(3)500 3039 y Fq(j)83 b(\024)762 2917 y Fg(\014)762
2966 y(\014)762 3016 y(\014)762 3066 y(\014)822 2977
y Fp(@)5 b(R)944 2991 y Fn(\027)t Fo(1)p 800 3018 247
4 v 800 3101 a Fp(@)g(')912 3115 y Fn(\027)t Fo(+1)1056
2917 y Fg(\014)1056 2966 y(\014)1056 3016 y(\014)1056
3066 y(\014)1099 3039 y Fq(j)p Fp(g)1167 3053 y Fn(\027)t
Fo(0)1246 3039 y Fq(j)25 b(\024)1564 2977 y Fv(1)p 1402
3018 370 4 v 1402 3101 a Fp(r)1443 3115 y Fn(\027)1506
3101 y Fq(\000)20 b Fp(r)1638 3115 y Fn(\027)t Fo(+1)1782
3039 y Fq(j)p Fp(R)1876 3053 y Fn(\027)t Fo(1)1954 3039
y Fq(j)1979 3054 y Fn(r)2011 3062 y Ff(\027)2050 3054
y Fn(;s)2103 3062 y Ff(\027)2141 3054 y Fn(;h)2202 3062
y Ff(\027)2244 3039 y Fq(j)p Fp(g)2312 3053 y Fn(\027)t
Fo(0)2391 3039 y Fq(j)608 3275 y(\024)1012 3214 y Fv(1)p
772 3254 527 4 v 772 3338 a(\()p Fp(r)848 3352 y Fn(\027)912
3338 y Fq(\000)g Fp(r)1044 3352 y Fn(\027)t Fo(+1)1177
3338 y Fv(\))p Fp(s)1255 3352 y Fn(\027)1308 3275 y Fq(j)p
Fp(R)1402 3289 y Fn(\027)1446 3275 y Fq(j)1471 3290 y
Fn(r)1503 3298 y Ff(\027)1541 3290 y Fn(;s)1594 3298
y Ff(\027)1632 3290 y Fn(;h)1693 3298 y Ff(\027)1735
3275 y Fq(j)p Fp(g)1803 3289 y Fn(\027)t Fo(0)1882 3275
y Fq(j)25 b Fv(=)g Fp(c)2067 3289 y Fo(1)2107 3275 y
Fp(\015)5 b(ss)2245 3289 y Fn(\027)2288 3275 y Fp(\026)2343
3238 y Fx(\000)p Fn(\034)2440 3275 y Fp(;)347 3551 y
Fq(j)p Fp(M)460 3565 y Fo(4)500 3551 y Fq(j)83 b(\024)858
3470 y Fg(X)762 3658 y Fx(j)p Fn(k)r Fx(j)p Fn(>T)10
b(\027)t Fo(+1)1090 3551 y Fq(j)p Fp(R)1185 3513 y Fo(1)1184
3573 y Fn(k)1221 3582 y Fm(1)1255 3573 y Fn(k)1292 3582
y Fm(2)1331 3551 y Fp(e)1373 3513 y Fn(i)p Fx(h)p Fn(k)1461
3522 y Fm(1)1496 3513 y Fn(;)p Fo(\012)1567 3522 y Fm(1)1601
3513 y Fx(i)p Fn(t)p Fo(+)p Fn(i)p Fx(h)p Fn(k)1796 3522
y Fm(2)1832 3513 y Fn(;)p Fo(\012)1903 3522 y Fm(2)1937
3513 y Fx(i)p Fn(')2010 3522 y Ff(\027)s Fm(+1)2130 3551
y Fq(j)26 b(\024)f Fp(cT)2382 3510 y Fn(N)2438 3519 y
Fm(1)2472 3510 y Fo(+)p Fn(N)2583 3519 y Fm(2)2369 3576
y Fn(\027)t Fo(+1)2622 3551 y Fp(e)2664 3513 y Fx(\000)2729
3477 y Ff(r)2758 3492 y Fm(0)p 2729 3498 64 4 v 2746
3539 a(2)2803 3513 y Fn(T)2844 3522 y Ff(\027)s Fm(+1)2963
3551 y Fq(j)p Fp(R)3057 3565 y Fn(\027)t Fo(1)3136 3551
y Fq(j)3161 3566 y Fn(r)3193 3574 y Ff(\027)3232 3566
y Fn(;s)3285 3574 y Ff(\027)3322 3566 y Fn(;h)3383 3574
y Ff(\027)608 3836 y Fq(\024)83 b Fp(cT)867 3796 y Fn(N)923
3805 y Fm(1)958 3796 y Fo(+)p Fn(N)1069 3805 y Fm(2)854
3861 y Fn(\027)t Fo(+1)1107 3836 y Fp(e)1149 3799 y Fx(\000)1214
3762 y Ff(r)1243 3777 y Fm(0)p 1214 3784 V 1231 3825
a(2)1288 3799 y Fn(T)1329 3808 y Ff(\027)s Fm(+1)1479
3775 y Fv(1)p 1459 3815 86 4 v 1459 3899 a Fp(s)1502
3913 y Fn(\027)1554 3836 y Fq(j)p Fp(R)1648 3850 y Fn(\027)1692
3836 y Fq(j)1717 3851 y Fn(r)1749 3859 y Ff(\027)1787
3851 y Fn(;s)1840 3859 y Ff(\027)1878 3851 y Fn(;h)1939
3859 y Ff(\027)2006 3836 y Fq(\024)25 b Fp(c\015)5 b(ss)2279
3850 y Fn(\027)2322 3836 y Fp(:)165 4051 y Fv(Note)32
b(that)680 4247 y Fq(j)p Fp(f)750 4261 y Fn(\027)t Fo(1)828
4247 y Fq(j)26 b(\024)1059 4166 y Fg(X)975 4355 y Fx(j)p
Fn(k)r Fx(j\024)p Fn(T)1150 4364 y Ff(\027)s Fm(+1)1497
4186 y Fv(2)p 1289 4226 461 4 v 1289 4310 a Fp(\015)5
b(s)1384 4324 y Fn(\027)1427 4310 y Fv(\010\()p Fp(T)1581
4324 y Fn(\027)t Fo(+1)1714 4310 y Fv(\))1760 4247 y
Fq(j)p Fp(R)1854 4261 y Fn(\027)1897 4247 y Fq(j)1922
4262 y Fn(r)1954 4270 y Ff(\027)1993 4262 y Fn(;s)2046
4270 y Ff(\027)2084 4262 y Fn(;h)2145 4270 y Ff(\027)2187
4247 y Fp(e)2229 4210 y Fx(\000j)p Fn(k)r Fx(j)p Fo(\()p
Fn(r)2422 4218 y Ff(\027)2459 4210 y Fx(\000)p Fn(r)2546
4219 y Ff(\027)s Fm(+1)2662 4210 y Fo(\))2718 4247 y
Fq(\024)2824 4186 y Fv(2)p Fp(c)2908 4200 y Fo(1)2949
4186 y Fp(s)p 2824 4226 167 4 v 2859 4310 a(\026)2914
4283 y Fn(\034)3026 4247 y Fp(<)25 b Fv(1)p Fp(;)165
4518 y Fv(whence)30 b(w)m(e)h(obtain)g(the)f(estimate)623
4699 y Fq(j)p Fp(R)717 4713 y Fn(\027)t Fo(+1)851 4699
y Fq(j)876 4714 y Fn(r)908 4723 y Ff(\027)s Fm(+1)1023
4714 y Fn(;s)1076 4723 y Ff(\027)s Fm(+1)1191 4714 y
Fn(;h)1252 4723 y Ff(\027)s Fm(+1)827 4885 y Fq(\024)1123
4824 y Fv(1)p 991 4864 310 4 v 991 4954 a(1)21 b Fq(\000)1158
4917 y Fo(2)p Fn(c)1224 4926 y Fm(1)1258 4917 y Fn(s)p
1158 4933 134 4 v 1183 4985 a(\026)1225 4966 y Ff(\034)1311
4766 y Fg(\024)1354 4885 y Fp(c)1393 4899 y Fo(1)1433
4885 y Fp(\015)5 b(ss)1571 4848 y Fo(2)1571 4908 y Fn(\027)1614
4885 y Fp(\026)1669 4848 y Fx(\000)p Fn(\034)1787 4885
y Fv(+)20 b Fp(c\015)5 b(ss)2055 4848 y Fo(2)2055 4908
y Fn(\027)2118 4885 y Fv(+)2209 4816 y Fg(\000)2247 4885
y Fp(c)2286 4899 y Fo(1)2325 4885 y Fp(\015)g(ss)2463
4899 y Fn(\027)2506 4885 y Fp(\026)2561 4848 y Fx(\000)p
Fn(\034)2679 4885 y Fv(+)20 b Fp(c\015)5 b(ss)2947 4899
y Fn(\027)2990 4816 y Fg(\001)3043 4885 y Fp(s)3086 4899
y Fn(\027)941 5169 y Fv(+)1042 5107 y Fp(\015)g(c)1133
5074 y Fo(2)1133 5130 y(1)1172 5107 y Fp(s)1215 5074
y Fo(2)1215 5130 y Fn(\027)1258 5107 y Fv(\()p Fp(s)1336
5121 y Fn(\027)1400 5107 y Fv(+)19 b Fp(s)1533 5121 y
Fn(\027)t Fo(+1)1666 5107 y Fv(\))p 1042 5148 661 4 v
1213 5234 a Fp(\026)1268 5207 y Fo(2)p Fn(\034)8 b Fo(\()p
Fn(\027)t Fo(+1\))1732 5169 y Fv(+)1833 5107 y Fp(\015)d(c)1924
5121 y Fo(1)1964 5107 y Fp(s)2007 5121 y Fn(\027)t Fo(+1)2140
5107 y Fp(s)2183 5121 y Fn(\027)2226 5107 y Fv(\()p Fp(s)2304
5121 y Fn(\027)2367 5107 y Fv(+)20 b Fp(s)2501 5121 y
Fn(\027)t Fo(+1)2634 5107 y Fv(\))p 1833 5148 837 4 v
2110 5234 a Fp(\026)2165 5207 y Fn(\034)8 b Fo(\()p Fn(\027)t
Fo(+1\))2679 5050 y Fg(\025)827 5408 y Fq(\024)1107 5346
y Fv(2)p Fp(\026)1207 5313 y Fn(\034)p 991 5387 376 4
v 991 5470 a Fp(\026)1046 5444 y Fn(\034)1109 5470 y
Fq(\000)20 b Fv(2)p Fp(c)1284 5484 y Fo(1)1324 5470 y
Fp(s)1392 5314 y Fg(\020)1442 5408 y Fp(c)1481 5422 y
Fo(1)1520 5408 y Fp(\026)1575 5370 y Fx(\000)p Fn(\034)1693
5408 y Fv(+)g Fp(c)h Fv(+)f Fp(c)1974 5370 y Fo(2)1974
5430 y(1)2014 5408 y Fp(\026)2069 5370 y Fx(\000)p Fo(2)p
Fn(\034)2222 5408 y Fv(+)g Fp(c)2352 5422 y Fo(1)2391
5314 y Fg(\021)2456 5408 y Fp(s\015)5 b(s)2594 5370 y
Fo(2)2594 5430 y Fn(\027)2662 5408 y Fq(\024)25 b Fp(\015)5
b(s)2853 5370 y Fo(2)2853 5430 y Fn(\027)t Fo(+1)2986
5408 y Fp(;)1891 5691 y Fv(12)p eop end
%%Page: 13 13
TeXDict begin 13 12 bop 165 337 a Fv(pro)m(vided)30 b(that)995
507 y(0)25 b Fp(<)g(s)g(<)1947 445 y(\026)2002 412 y
Fo(2\()p Fn(\024)p Fo(+)p Fn(\034)8 b Fo(\))p 1335 486
1509 4 v 1335 570 a Fv(2\()p Fp(c)1454 584 y Fo(1)1495
570 y Fp(\026)1550 544 y Fn(\034)1613 570 y Fv(+)20 b
Fp(c\026)1798 544 y Fo(2)p Fn(\034)1896 570 y Fv(+)g
Fp(c)2026 539 y Fo(2)2026 595 y(1)2086 570 y Fv(+)g Fp(c)2216
584 y Fo(1)2256 570 y Fp(\026)2311 544 y Fo(2)p Fn(\034)2409
570 y Fv(+)g Fp(c)2539 584 y Fo(1)2579 570 y Fp(\026)2634
544 y Fo(2)p Fn(\024)p Fo(+)p Fn(\034)2808 570 y Fv(\))2853
507 y Fp(:)165 743 y Fv(By)35 b(induction,)i(w)m(e)f(can)f(pro)m(v)m(e)
h(that)g(for)f(an)m(y)h Fp(\027)j Fq(\025)34 b Fv(0)h(there)h(is)f(a)h
(sequence)2921 717 y Fg(e)2897 743 y Fq(F)2962 757 y
Fn(\027)3039 743 y Fv(=)d(\()p Fq(S)3233 757 y Fn(\027)3276
743 y Fp(;)15 b Fv(id)24 b(+)f Fp(\036)p Fv(\))36 b(of)165
856 y(transformations)30 b(suc)m(h)g(that)h(\(2)p Fp(:)p
Fv(22\))i(and)d(\(2)p Fp(:)p Fv(10\))1892 870 y Fn(\027)t
Fo(+1)2058 856 y Fv(are)h(ful\014lled)e(if)173 1126 y(0)c
Fp(<)g(s)g(<)g Fv(min)670 982 y Fg(\()811 1064 y Fv(1)p
772 1105 125 4 v 772 1188 a(2)p Fp(c)856 1202 y Fo(1)906
1126 y Fv(\()p Fp(\026)996 1088 y Fn(\024)1061 1126 y
Fq(\000)20 b Fp(\026)1207 1088 y Fo(2)p Fn(\024)1287
1126 y Fv(\);)1393 1064 y Fp(\026)1448 1031 y Fn(\034)p
1373 1105 139 4 v 1373 1188 a Fp(c)1412 1202 y Fo(1)1452
1188 y Fp(!)1521 1126 y Fv(;)1594 1064 y Fp(h)p 1572
1105 98 4 v 1572 1188 a Fv(4)p Fp(\015)1679 1126 y Fv(;)1795
1064 y(3)p Fp(\026)1895 1031 y Fn(\024)p 1730 1105 275
4 v 1730 1188 a Fp(c)1769 1202 y Fo(2)1829 1188 y Fv(+)g(4)p
Fp(c)2014 1126 y Fv(;)2677 1064 y Fp(\026)2732 1031 y
Fo(2\()p Fn(\024)p Fo(+)p Fn(\034)8 b Fo(\))p 2065 1105
1509 4 v 2065 1189 a Fv(2\()p Fp(c)2184 1203 y Fo(1)2224
1189 y Fp(\026)2279 1163 y Fn(\034)2342 1189 y Fv(+)20
b Fp(c\026)2527 1163 y Fo(2)p Fn(\034)2626 1189 y Fv(+)g
Fp(c)2756 1158 y Fo(2)2756 1214 y(1)2816 1189 y Fv(+)g
Fp(c)2946 1203 y Fo(1)2986 1189 y Fp(\026)3041 1163 y
Fo(2)p Fn(\034)3139 1189 y Fv(+)g Fp(c)3269 1203 y Fo(1)3309
1189 y Fp(\026)3364 1163 y Fo(2)p Fn(\024)p Fo(+)p Fn(\034)3538
1189 y Fv(\))3608 982 y Fg(\))3675 1126 y Fp(:)165 1390
y Fv(It)30 b(remains)g(to)i(establish)e(the)h(uniform)e(con)m(v)m
(ergence)k(of)d(the)h(sequence)750 1595 y Fq(S)812 1557
y Fn(\027)880 1595 y Fv(:=)26 b Fq(S)1057 1609 y Fo(0)1116
1595 y Fq(\016)21 b(S)1237 1609 y Fo(1)1297 1595 y Fq(\016)f
Fp(:)15 b(:)g(:)21 b Fq(\016)g(S)1609 1609 y Fn(\027)1703
1595 y Fv(:)51 b Fp(D)1854 1609 y Fn(r)1886 1618 y Ff(\027)s
Fm(+1)2001 1609 y Fn(;s)2054 1618 y Ff(\027)s Fm(+1)2193
1595 y Fq(\002)20 b Fp(O)2353 1610 y Fn(h)2394 1619 y
Ff(\027)s Fm(+1)2539 1595 y Fq(\000)-15 b(!)25 b Fp(D)2786
1609 y Fn(r)n(;s)2893 1595 y Fq(\002)20 b Fp(O)3053 1610
y Fn(h)3098 1595 y Fp(:)165 1799 y Fv(It)30 b(follo)m(ws)i(from)e(\(2)p
Fp(:)p Fv(21\))i(that)739 2003 y Fq(j)p Fp(D)s Fq(S)897
2017 y Fn(\037)945 2003 y Fv(\()p Fq(S)1035 2017 y Fn(\037)p
Fo(+1)1194 2003 y Fq(\016)20 b(\001)15 b(\001)g(\001)22
b(\016)e(S)1506 2017 y Fn(\027)1550 2003 y Fv(\))p Fq(j)25
b(\024)g Fv(1)c(+)f Fp(c)1927 2017 y Fo(2)1967 2003 y
Fp(\026)2022 1966 y Fo(\()p Fn(\024)p Fx(\000)p Fn(\034)8
b Fo(\))p Fn(\037)2259 2003 y Fp(;)106 b(\037)25 b Fv(=)g(0)p
Fp(;)15 b Fv(1)p Fp(;)g(:)g(:)g(:)j(;)d(\027)26 b Fq(\000)20
b Fv(1)p Fp(:)165 2207 y Fv(W)-8 b(e)31 b(infer)408 2412
y Fq(j)p Fp(D)s Fq(S)573 2374 y Fn(\027)t Fx(\000)p Fo(1)707
2412 y Fq(j)25 b(\024)g Fv(\(1)c(+)f Fp(c)1084 2426 y
Fo(2)1124 2412 y Fv(\))15 b Fq(\001)g(\001)g(\001)1295
2317 y Fg(\020)1345 2412 y Fv(1)21 b(+)f Fp(c)1541 2426
y Fo(2)1580 2412 y Fp(\026)1635 2374 y Fo(\()p Fn(\024)p
Fx(\000)p Fn(\034)8 b Fo(\)\()p Fn(\027)t Fx(\000)p Fo(1\))2013
2317 y Fg(\021)2088 2412 y Fq(\024)25 b Fp(e)2226 2374
y Fn(c)2257 2383 y Fm(2)2291 2374 y Fo(\(1+)p Fn(\026)2450
2351 y Fm(\()p Ff(\024)p Fl(\000)p Ff(\034)6 b Fm(\))2622
2374 y Fo(+)p Fx(\001\001\001)o Fo(+)p Fn(\026)2833 2351
y Fm(\()p Ff(\024)p Fl(\000)p Ff(\034)g Fm(\)\()p Ff(\027)s
Fl(\000)p Fm(1\))3165 2374 y Fo(\))3222 2412 y Fq(\024)25
b Fp(e)3360 2374 y Fo(2)p Fn(c)3426 2383 y Fm(2)165 2626
y Fv(and)30 b(hence)629 2831 y Fq(jS)716 2793 y Fn(\027)779
2831 y Fq(\000)20 b(S)932 2793 y Fn(\027)t Fx(\000)p
Fo(1)1065 2831 y Fq(j)26 b(\024)f(jS)1299 2793 y Fn(\027)t
Fx(\000)p Fo(1)1432 2831 y Fv(\()p Fq(S)1522 2845 y Fn(\027)1566
2831 y Fv(\))20 b Fq(\000)g(S)1774 2793 y Fn(\027)t Fx(\000)p
Fo(1)1907 2831 y Fq(j)26 b(\024)f Fp(e)2096 2793 y Fo(2)p
Fn(c)2162 2802 y Fm(2)2201 2831 y Fq(jS)2281 2845 y Fn(\027)2345
2831 y Fq(\000)19 b Fp(id)p Fq(j)27 b(\024)e Fv(2)p Fp(c)2745
2845 y Fo(2)2785 2831 y Fp(e)2827 2793 y Fo(2)p Fn(c)2893
2802 y Fm(2)2932 2831 y Fp(\026)2987 2793 y Fo(\()p Fn(\024)p
Fx(\000)p Fn(\034)8 b Fo(\))p Fn(\027)3219 2831 y Fp(:)165
3035 y Fv(The)25 b(same)i(inequalit)m(y)g(holds)f(for)g
Fp(\027)31 b Fv(=)24 b(0)j(if)f(w)m(e)g(de\014ne)g Fq(S)2129
3002 y Fx(\000)p Fo(1)2248 3035 y Fv(:=)f(id.)39 b(This)26
b(implies)g(that)g(the)h(sequence)1431 3295 y Fq(S)1493
3257 y Fn(\027)1561 3295 y Fv(=)e Fq(S)1719 3257 y Fo(0)1779
3295 y Fv(+)1910 3189 y Fn(\027)1870 3214 y Fg(X)1873
3396 y Fn(i)p Fo(=0)1990 3295 y Fv(\()p Fq(S)2087 3257
y Fn(i)2135 3295 y Fq(\000)20 b(S)2288 3257 y Fn(i)p
Fx(\000)p Fo(1)2406 3295 y Fv(\))165 3567 y(con)m(v)m(erges)26
b(uniformly)e(on)h Fp(D)1181 3557 y Ff(r)1210 3572 y
Fm(0)p 1181 3579 64 4 v 1197 3620 a(2)1254 3594 y Fn(;)p
Fo(0)1322 3567 y Fq(\002)9 b Fp(A)1470 3581 y Fn(\015)1514
3567 y Fv(.)39 b(This)24 b(domain)g(has)h(zero)g(width)f(in)g(the)h
Fp(I)7 b Fv(-direction,)27 b(whence)165 3696 y(only)32
b Fp(')p Fv(,)h Fp(t)e Fv(and)g Fp(a)h Fv(can)g(v)-5
b(ary)32 b(\(the)g(latter)h(only)f(within)g(the)g(Can)m(tor)g(set)g
Fp(A)2781 3710 y Fn(\015)2826 3696 y Fv(\).)45 b(T)-8
b(o)32 b(extend)g(the)g(limit)165 3809 y(function)i Fq(S)587
3776 y Fx(1)696 3809 y Fv(to)h(a)g(v)-5 b(alid)34 b(transformation)h(w)
m(e)g(use)f(that)h(the)f Fq(S)2453 3823 y Fn(\027)2531
3809 y Fv(are)h(de\014ned)e(in)h(\(2)p Fp(:)p Fv(11\))i(as)f(a\016ne)
165 3922 y(transformations)e(in)g Fp(I)7 b Fv(,)34 b(linear)g(p)s
(olynomials)g(with)e(co)s(e\016cien)m(ts)j(dep)s(ending)d(on)h
Fp(')p Fv(,)i Fp(t)e Fv(and)g Fp(a)p Fv(.)49 b(This)165
4035 y(mak)m(es)44 b(the)f(comp)s(ositions)h Fq(S)1239
4002 y Fn(\027)1325 4035 y Fv(a\016ne)f(in)f Fp(I)51
b Fv(as)43 b(w)m(ell,)k(and)c(w)m(e)g(just)g(sho)m(w)m(ed)g(that)h(the)
f(constan)m(t)165 4148 y(co)s(e\016cien)m(ts)32 b(con)m(v)m(erge)g(to)g
Fq(S)1170 4115 y Fx(1)1244 4148 y Fv(.)41 b(The)30 b(linear)g(co)s
(e\016cien)m(ts)j(are)d(giv)m(en)i(b)m(y)e(the)g(deriv)-5
b(ativ)m(es)1093 4390 y Fq(T)1166 4352 y Fn(\027)1209
4390 y Fv(\()p Fp(')1303 4404 y Fn(\027)t Fo(+1)1437
4390 y Fp(;)15 b(t;)g(a)1598 4404 y Fn(\027)t Fo(+1)1732
4390 y Fv(\))26 b(=)1933 4328 y Fp(@)5 b Fq(S)2048 4296
y Fn(\027)p 1899 4369 227 4 v 1899 4452 a Fp(@)g(I)1992
4466 y Fn(\027)t Fo(+1)2135 4390 y Fv(\(0)p Fp(;)15 b(')2314
4404 y Fn(\027)t Fo(+1)2449 4390 y Fp(;)g(t;)g(a)2610
4404 y Fn(\027)t Fo(+1)2744 4390 y Fv(\))165 4636 y(at)29
b Fp(I)314 4650 y Fn(\027)t Fo(+1)472 4636 y Fv(=)c(0)k(and)f(to)h(sho)
m(w)f(con)m(v)m(ergence)j(w)m(e)e(estimate)h(ho)m(w)e(m)m(uc)m(h)g
(these)h(di\013er)f(from)g(the)h(iden)m(tit)m(y)165 4749
y(in)e Fp(I)308 4763 y Fn(\027)t Fo(+1)441 4749 y Fv(.)40
b(The)27 b(ab)s(o)m(v)m(e)h(considerations)g(applied)g(to)g
Fq(T)2029 4716 y Fn(\027)2100 4749 y Fv(yield)f(again)i(the)e(desired)g
(con)m(v)m(ergence;)k(here)165 4861 y(w)m(e)g(use)f(that)h(the)f
(second)h(deriv)-5 b(ativ)m(e)32 b(with)e(resp)s(ect)g(to)h
Fp(I)2189 4875 y Fn(\027)t Fo(+1)2353 4861 y Fv(v)-5
b(anishes.)40 b(No)m(w)31 b(put)1096 5066 y Fq(S)1151
5080 y Fx(1)1226 5066 y Fv(\()p Fp(I)7 b(;)15 b(';)g(t;)g(a)p
Fv(\))27 b(:=)e Fq(S)1813 5028 y Fx(1)1888 5066 y Fv(\()p
Fp(';)15 b(t;)g(a)p Fv(\))22 b(+)e Fq(T)2364 5028 y Fx(1)2438
5066 y Fv(\()p Fp(';)15 b(t;)g(a)p Fv(\))p Fp(I)165 5270
y Fv(whence)32 b Fq(S)540 5284 y Fx(1)646 5270 y Fv(is)g(the)g(desired)
g(transformation)g(\(2.4\))i(and)d(\(2.6\))j(follo)m(ws)f(from)e(\(2)p
Fp(:)p Fv(10\))3191 5284 y Fn(\027)3237 5270 y Fv(.)45
b(This)31 b(com-)165 5383 y(pletes)g(the)g(pro)s(of.)2835
b Fq(u)-61 b(t)1891 5691 y Fv(13)p eop end
%%Page: 14 14
TeXDict begin 14 13 bop 165 337 a Fj(Remark)35 b(2.2)46
b Fv(The)26 b(Bruno)g(condition)i(\(1)p Fp(:)p Fv(4\))g(is)f(w)m(eak)m
(er)g(than)g(a)g(Diophan)m(tine)g(condition)h(with)e(the)165
450 y(same)31 b Fp(\015)h(>)26 b Fv(0)32 b(and)e(it)i(follo)m(ws)g(for)
f Fp(N)1427 464 y Fo(2)1493 450 y Fv(=)26 b(1)32 b(similarly)f(to)h
(Lemma)f(2)h(in)f([2])h(that)f(for)g(\014xed)g Fp(\017)26
b(>)g Fv(0)32 b(the)165 562 y(measure)e(of)341 762 y
Fp(A)409 776 y Fn(\017L)515 762 y Fv(=)611 643 y Fg(\032)673
762 y Fp(\013)c Fq(2)f Fp(\017J)34 b Fv(:)26 b Fq(jh)p
Fp(k)1122 776 y Fo(1)1162 762 y Fp(;)15 b Fv(\012)1268
776 y Fo(1)1308 762 y Fq(i)20 b Fv(+)g Fq(h)p Fp(k)1536
776 y Fo(2)1576 762 y Fp(;)15 b(\013)p Fv(\012)1740 776
y Fo(2)1780 762 y Fq(ij)26 b(\025)f Fp(\017L)p Fv(\010\()p
Fq(j)p Fp(k)s Fq(j)p Fv(\))51 b(for)31 b(all)g(0)26 b
Fq(6)p Fv(=)e Fp(k)29 b Fq(2)c Fh(Z)2997 729 y Fn(N)3053
738 y Fm(1)3088 729 y Fo(+)p Fn(N)3199 738 y Fm(2)3237
643 y Fg(\033)3476 762 y Fv(\(2.25\))165 985 y(where)k(our)h(result)f
(do)s(es)h(not)g(apply)f(tends)h(to)g Fp(\017)g Fv(as)g
Fp(L)25 b Fq(#)h Fv(0,)k(with)g(\010\()p Fp(t)p Fv(\))g(an)g(appro)m
(ximation)g(function)165 1098 y(as)g(in)h(De\014nition)g(1.2)g(and)f
Fp(J)k Fq(\032)25 b Fv(\(0)p Fp(;)15 b Fv(+)p Fq(1)p
Fv(\))32 b(a)e(unit)g(in)m(terv)-5 b(al.)42 b(This)30
b(extends)g(to)h Fp(N)3012 1112 y Fo(2)3077 1098 y Fq(\025)25
b Fv(2.)165 1528 y Fd(2.2)112 b(Hamiltonian)39 b(systems)165
1700 y Fv(Consider)29 b(the)i(Hamiltonian)h(system)1067
1902 y(_)1046 1925 y Fp(I)g Fv(=)25 b Fq(\000)1295 1863
y Fp(@)5 b(H)i Fv(\()p Fp(I)g(;)15 b(';)g(t;)g(a)p Fv(\))p
1295 1904 516 4 v 1496 1987 a Fp(@)5 b(')1820 1925 y(;)131
b Fv(_)-49 b Fp(')25 b Fv(=)g Fp(a)c Fv(+)2302 1863 y
Fp(@)5 b(H)i Fv(\()p Fp(I)g(;)15 b(';)g(t;)g(a)p Fv(\))p
2302 1904 V 2509 1987 a Fp(@)5 b(I)3476 1925 y Fv(\(2.26\))165
2146 y(on)41 b Fh(R)27 b Fq(\002)h Fh(T)41 b Fv(with)g(a)h
(one-dimensional)g(parameter)f Fp(a)p Fv(.)74 b(W)-8
b(e)42 b(assume)f(that)h(for)f(\014xed)g Fp(I)48 b Fv(and)40
b Fp(a)i Fv(w)m(e)165 2259 y(ha)m(v)m(e)34 b Fp(H)7 b
Fv(\()p Fp(I)g(;)15 b Fq(\001)p Fp(;)g Fq(\001)p Fp(;)g(a)p
Fv(\))31 b Fq(2)d Fp(Q)987 2273 y Fn(r)1025 2259 y Fv(\(\012)1126
2273 y Fo(1)1166 2259 y Fp(;)15 b Fv(\012)1272 2273 y
Fo(2)1311 2259 y Fv(\))33 b(with)f(\012)1654 2273 y Fo(1)1722
2259 y Fv(=)d(\()p Fp(!)1914 2273 y Fo(1)1953 2259 y
Fp(;)15 b(:)g(:)g(:)i(;)e(!)2212 2273 y Fn(N)2268 2282
y Fm(1)2306 2259 y Fv(\))30 b Fq(2)e Fh(R)2520 2226 y
Fn(N)2576 2235 y Fm(1)2647 2259 y Fv(and)k(\012)2892
2273 y Fo(2)2960 2259 y Fv(=)d Fp(!)3117 2273 y Fn(N)3173
2282 y Fm(1)3207 2273 y Fo(+1)3330 2259 y Fq(2)g Fh(R)p
Fv(.)47 b(The)165 2372 y(corresp)s(onding)29 b(shell)i(function)1336
2345 y Fg(e)1313 2372 y Fp(H)7 b Fv(\()p Fp(I)g(;)15
b(';)g(\022)s(;)g(a)p Fv(\))32 b(is)e(real)h(analytic)h(in)e
Fp(D)2613 2386 y Fn(r)n(;s)2720 2372 y Fq(\002)20 b Fp(O)2880
2387 y Fn(h)2955 2372 y Fv(and)30 b(satis\014es)1656
2554 y Fq(j)1705 2527 y Fg(e)1681 2554 y Fp(H)7 b Fq(j)1789
2569 y Fn(r)n(;s;h)1961 2554 y Fp(<)25 b(\015)5 b(s)2152
2516 y Fo(2)2192 2554 y Fp(:)1259 b Fv(\(2.27\))165 2736
y(F)-8 b(urthermore)31 b(w)m(e)g(assume)g(that)h Fp(H)h
Fv(=)26 b Fp(H)7 b Fv(\()p Fp(I)g(;)15 b(';)g(t;)g(a)p
Fv(\))33 b(has)e(for)g Fp(I)i Fv(=)26 b(0)31 b(zero)h(a)m(v)m(erage)i
(with)c(resp)s(ect)h(to)165 2849 y Fp(')g Fv(and)60 b
Fp(t)p Fv(.)165 3040 y Fj(Theorem)35 b(2.3)46 b Fi(Under)28
b(the)h(ab)-5 b(ove)29 b(assumptions)h(and)g(if)e(the)g(Bruno)h(c)-5
b(ondition)30 b(\(1.4\))f(holds,)i(ther)-5 b(e)165 3152
y(is)40 b(an)g Fp(s)450 3120 y Fx(\003)529 3152 y Fi(such)h(that)g(for)
g(any)f(p)-5 b(ositive)41 b Fp(s)e(<)f(s)1840 3120 y
Fx(\003)1919 3152 y Fi(ther)-5 b(e)41 b(is)f(a)h(function)f
Fp(a)2758 3166 y Fo(0)2836 3152 y Fv(:)f Fp(A)2968 3166
y Fn(\015)3051 3152 y Fq(\000)-15 b(!)39 b Fh(R)g Fi(satisfying)165
3265 y Fq(j)p Fp(a)238 3279 y Fo(0)278 3265 y Fv(\()p
Fp(\013)p Fv(\))21 b Fq(\000)f Fp(\013)p Fq(j)26 b Fp(<)f(h)33
b Fi(for)g(al)5 b(l)33 b Fp(\013)26 b Fq(2)f Fp(A)1321
3279 y Fn(\015)1398 3265 y Fi(and)33 b(a)g(c)-5 b(anonic)g(al)35
b(change)e(of)g(variables)911 3448 y Fp(I)f Fv(=)25 b
Fp(\045)20 b Fv(+)g Fp(v)s Fv(\()p Fp(\045;)15 b( )s(;)g(\022)s(;)g
(\013)p Fv(\))p Fp(;)111 b(')26 b Fv(=)f Fp( )e Fv(+)d
Fp(u)p Fv(\()p Fp( )s(;)15 b(\022)s(;)g(\013)p Fv(\))p
Fp(;)110 b(\013)26 b Fq(2)f Fp(A)2918 3462 y Fn(\015)3476
3448 y Fv(\(2.28\))165 3630 y Fi(which)33 b(tr)-5 b(ansforms)36
b(system)d(\(2.26\))h(with)g Fp(a)25 b Fv(=)g Fp(a)1862
3644 y Fo(0)1901 3630 y Fv(\()p Fp(\013)p Fv(\))34 b
Fi(into)f(a)g(system)1043 3860 y Fv(_)-44 b Fp(\045)25
b Fv(=)g Fq(\000)1273 3799 y Fp(@)5 b(K)i Fv(\()p Fp(\045;)15
b( )s(;)g(t;)g(\013)p Fv(\))p 1273 3839 530 4 v 1480
3922 a Fp(@)5 b( )1813 3860 y(;)1975 3836 y Fv(_)1946
3860 y Fp( )29 b Fv(=)c Fp(\013)20 b Fv(+)2309 3799 y
Fp(@)5 b(K)i Fv(\()p Fp(\045;)15 b( )s(;)g(t;)g(\013)p
Fv(\))p 2309 3839 V 2524 3922 a Fp(@)5 b(\045)3476 3860
y Fv(\(2.29\))165 4081 y Fi(such)33 b(that)887 4165 y
Fp(@)5 b(K)i Fv(\(0)p Fp(;)15 b( )s(;)g(t;)g(\013)p Fv(\))p
887 4205 529 4 v 1094 4289 a Fp(@)5 b( )1451 4226 y Fv(=)1557
4165 y Fp(@)g(K)i Fv(\(0)p Fp(;)15 b( )s(;)g(t;)g(\013)p
Fv(\))p 1557 4205 V 1771 4289 a Fp(@)5 b(\045)2120 4226
y Fv(=)2226 4165 y Fp(@)2279 4132 y Fo(2)2319 4165 y
Fp(K)i Fv(\(0)p Fp(;)15 b( )s(;)g(t;)g(\013)p Fv(\))p
2226 4205 568 4 v 2394 4289 a Fp(@)5 b(\045)15 b(@)5
b( )2829 4226 y Fv(=)25 b(0)p Fp(:)481 b Fv(\(2.30\))165
4461 y(It)30 b(follo)m(ws)i(that)f(for)f(eac)m(h)h Fp( )1161
4475 y Fo(0)1231 4461 y Fv(the)g(system)g(\(2.26\))h(admits)f(the)f
(quasi-p)s(erio)s(dic)g(solution)602 4643 y Fp(I)7 b
Fv(\()p Fp(t)p Fv(\))26 b(=)f Fp(v)s Fv(\(0)p Fp(;)15
b( )1100 4657 y Fo(0)1161 4643 y Fv(+)20 b Fp(\013t;)15
b Fv(\012)1449 4657 y Fo(1)1489 4643 y Fp(t;)g(\013)p
Fv(\))p Fp(;)108 b(')p Fv(\()p Fp(t)p Fv(\))26 b(=)f
Fp( )2131 4657 y Fo(0)2191 4643 y Fv(+)20 b Fp(\013t)g
Fv(+)g Fp(u)p Fv(\(0)p Fp(;)15 b( )2715 4657 y Fo(0)2776
4643 y Fv(+)20 b Fp(\013t;)15 b Fv(\012)3064 4657 y Fo(1)3104
4643 y Fp(t;)g(\013)p Fv(\))165 4825 y(with)30 b(frequency)g(v)m
(ectors)i(\012)1159 4839 y Fo(1)1228 4825 y Fv(and)e
Fp(\013)p Fv(\012)1529 4839 y Fo(2)1568 4825 y Fv(.)165
5034 y Fi(Pr)-5 b(o)g(of.)50 b Fv(W)-8 b(e)34 b(use)e(the)h(shell)g
(function)1522 5008 y Fg(e)1499 5034 y Fp(H)39 b Fv(to)34
b(de\014ne)e(a)h(Hamiltonian)h(system)f(in)g Fp(N)3082
5048 y Fo(1)3143 5034 y Fv(+)21 b(1)34 b(degrees)f(of)165
5147 y(freedom.)40 b(T)-8 b(o)30 b(this)e(end)h(w)m(e)g(in)m(tro)s
(duce)g(the)h(v)-5 b(ariables)29 b Fp(E)2158 5161 y Fo(1)2198
5147 y Fp(;)15 b(:)g(:)g(:)i(;)e(E)2467 5161 y Fn(N)2523
5170 y Fm(1)2591 5147 y Fv(canonically)31 b(conjugate)f(to)g(the)165
5260 y(angles)h Fp(\022)481 5274 y Fo(1)520 5260 y Fp(;)15
b(:)g(:)g(:)i(;)e(\022)765 5274 y Fn(N)821 5283 y Fm(1)890
5260 y Fv(and)30 b(de\014ne)1053 5416 y Fg(b)1029 5442
y Fp(H)7 b Fv(\()p Fp(I)g(;)15 b(E)5 b(;)15 b(';)g(\022)s(;)g(a)p
Fv(\))28 b(:=)d Fp(aI)j Fv(+)19 b Fq(h)p Fv(\012)2070
5456 y Fo(1)2110 5442 y Fp(;)c(E)5 b Fq(i)21 b Fv(+)2393
5416 y Fg(e)2369 5442 y Fp(H)7 b Fv(\()p Fp(I)g(;)15
b(';)g(\022)s(;)g(a)p Fv(\))1891 5691 y(14)p eop end
%%Page: 15 15
TeXDict begin 15 14 bop 165 337 a Fv(with)30 b(resulting)g(equations)h
(of)g(motion)974 579 y(_)953 602 y Fp(I)91 b Fv(=)82
b Fq(\000)1318 540 y Fp(@)1395 514 y Fg(e)1371 540 y
Fp(H)7 b Fv(\()p Fp(I)g(;)15 b(';)g(\022)s(;)g(a)p Fv(\))p
1318 581 529 4 v 1526 664 a Fp(@)5 b(')1856 602 y(;)2018
579 y Fv(_)1987 602 y Fp(E)56 b Fv(=)50 b Fq(\000r)2378
617 y Fn(\022)2440 575 y Fg(e)2417 602 y Fp(H)7 b Fv(\()p
Fp(I)g(;)15 b(';)g(\022)s(;)g(a)p Fv(\))p Fp(;)966 863
y Fv(_)-50 b Fp(')84 b Fv(=)e Fp(a)21 b Fv(+)1406 801
y Fp(@)1483 775 y Fg(e)1459 801 y Fp(H)8 b Fv(\()p Fp(I)f(;)15
b(';)g(\022)s(;)g(a)p Fv(\))p 1406 842 V 1620 925 a Fp(@)5
b(I)1944 863 y(;)2093 839 y Fv(_)2076 863 y Fp(\022)52
b Fv(=)f(\012)2359 877 y Fo(1)2398 863 y Fp(:)165 1093
y Fv(T)-8 b(o)41 b(this)g(situation)h(w)m(e)g(apply)e(the)h(Main)h
(Theorem)f(1.7)h(of)f([16)q(])g(with)g(unp)s(erturb)s(ed)c(part)k
Fp(aI)34 b Fv(+)165 1206 y Fq(h)p Fv(\012)266 1220 y
Fo(1)305 1206 y Fp(;)15 b(E)5 b Fq(i)23 b Fv(+)f(a)m(v)r(\()719
1180 y Fg(e)695 1206 y Fp(H)8 b Fv(\)\()p Fp(I)f(;)15
b(a)p Fv(\))34 b(and)f(p)s(erturbation)1792 1180 y Fg(e)1769
1206 y Fp(H)7 b Fv(\()p Fp(I)g(;)15 b(';)g(\022)s(;)g(a)p
Fv(\))23 b Fq(\000)f Fv(a)m(v)r(\()2509 1180 y Fg(e)2485
1206 y Fp(H)7 b Fv(\)\()p Fp(I)g(;)15 b(a)p Fv(\).)51
b(Since)33 b(the)g(latter)h(do)s(es)165 1319 y(not)c(dep)s(end)f(on)h
Fp(E)36 b Fv(the)31 b(ensuing)e(transformation)1360 1523
y(\()p Fp(I)7 b(;)15 b(E)5 b(;)15 b(';)g(\022)s(;)g(a)p
Fv(\))28 b Fq(7!)d Fv(\()p Fp(\045;)15 b(F)s(;)g( )s(;)g(\022)s(;)g
(\013)p Fv(\))165 1727 y(k)m(eeps)31 b Fp(\022)h Fv(\014xed)e(and)g
(yields)1022 1905 y Fg(c)1016 1932 y Fp(K)7 b Fv(\()p
Fp(\045;)15 b(F)s(;)g( )s(;)g(\022)s(;)g(\013)p Fv(\))28
b(=)d Fp(\013\045)20 b Fv(+)g Fq(h)p Fv(\012)2045 1946
y Fo(1)2085 1932 y Fp(;)15 b(F)e Fq(i)21 b Fv(+)2348
1905 y Fg(f)2343 1932 y Fp(K)6 b Fv(\()p Fp(\045;)15
b( )s(;)g(\022)s(;)g(\013)p Fv(\))p Fp(:)165 2136 y Fv(The)27
b(resulting)h(equations)g(of)g(motion)h(are)f(again)h(indep)s(enden)m
(t)d(of)i Fp(F)41 b Fv(and)27 b(inserting)h Fp(\022)f
Fv(=)e(\012)3411 2150 y Fo(1)3450 2136 y Fp(t)j Fv(leads)165
2249 y(to)j(the)g(desired)e(system)i(\(2)p Fp(:)p Fv(29\).)2350
b Fq(u)-61 b(t)165 2461 y Fj(Remark)35 b(2.4)46 b Fv(F)-8
b(or)26 b(\012)965 2475 y Fo(2)1029 2461 y Fq(2)f Fh(R)1175
2428 y Fn(N)1231 2437 y Fm(2)1295 2461 y Fv(with)g Fp(N)1570
2475 y Fo(2)1635 2461 y Fq(\025)g Fv(2)g(one)h(can)f(similarly)h
(de\014ne)e(a)i(Hamiltonian)g(system)f(in)165 2574 y
Fp(N)238 2588 y Fo(1)298 2574 y Fv(+)20 b Fp(N)462 2588
y Fo(2)532 2574 y Fv(degrees)31 b(of)g(freedom,)g(with)g
Fp(N)1608 2588 y Fo(2)1678 2574 y Fv(additional)h(angular)e(v)-5
b(ariables)2821 2547 y Fg(e)2814 2574 y Fp(\022)33 b
Fv(to)e(allo)m(w)h(for)3383 2547 y Fg(e)3376 2574 y Fp(\022)c
Fv(=)e(\012)3610 2588 y Fo(2)3649 2574 y Fp(')165 2687
y Fv(and)k(conjugate)h(actions)h Fp(J)i Fq(2)25 b Fh(R)1292
2654 y Fn(N)1348 2663 y Fm(2)1387 2687 y Fv(.)165 3073
y Fr(3)135 b(Applications)165 3276 y Fv(In)39 b(this)i(section)g(w)m(e)
g(apply)f(Theorems)g(2.1)h(and)f(2.3)h(to)g(non-autonomous)f(v)m(ector)
i(\014elds)e(in)g(the)165 3389 y(plane.)52 b(Sp)s(eci\014cally)-8
b(,)36 b(w)m(e)e(are)h(in)m(terested)g(in)f(dynamical)g(stabilit)m(y)i
(of)e(the)g(solution)h(\()p Fp(x)p Fv(\()p Fp(t)p Fv(\))p
Fp(;)15 b(y)s Fv(\()p Fp(t)p Fv(\)\))33 b Fq(\021)165
3502 y Fv(\(0)p Fp(;)15 b Fv(0\))38 b(that)e(sta)m(ys)h(at)g(the)f
(origin)h(for)e(all)i(times.)58 b(The)36 b(main)g(idea)g(is)g(as)h
(follo)m(ws:)53 b(the)36 b(families)h(of)165 3615 y(quasi-p)s(erio)s
(dic)30 b(solutions)h(constructed)g(in)g(the)g(previous)f(section)i
(determine)f(in)m(v)-5 b(arian)m(t)31 b(cylinders)165
3728 y(that)h(are)h(b)s(oundaries)d(of)i(tubular)f(neigh)m(b)s(ourho)s
(o)s(ds)f(around)h(the)h Fp(t)p Fv(-axis.)46 b(Suc)m(h)31
b(cylinders)g(con\014ne)165 3841 y(in)m(tegral)c(curv)m(es,)h(and)d(so)
h(the)g(stabilit)m(y)i(follo)m(ws.)40 b(W)-8 b(e)27 b(generalize)h
(results)e(that)g(ha)m(v)m(e)i(b)s(een)d(obtained)165
3953 y(in)c([7,)h(8,)g(2,)f(9)q(],)i(where)e(the)g(cases)i(of)e(rev)m
(ersible)h(and)e(Hamiltonian)j(systems)e(w)m(ere)h(treated)g
(separately)165 4066 y(but)28 b(with)h(v)m(ery)g(similar)h(pro)s(ofs.)
39 b(Using)29 b(the)h(Lie-algebraic)h(approac)m(h)f(of)f([10)q(,)g(4)q
(])g(w)m(e)g(giv)m(e)i(a)e(uni\014ed)165 4179 y(pro)s(of,)34
b(bringing)f(out)h(more)g(clearly)h(the)e(in)m(timate)j(relation)f(b)s
(et)m(w)m(een)f(these)g(results.)50 b(In)33 b(order)g(to)165
4292 y(equally)38 b(allo)m(w)h(for)e(a)g(uni\014ed)f(form)m(ulation)i
(w)m(e)g(sp)s(eak)f(of)h(a)f Fi(c)-5 b(onservative)38
b Fv(v)m(ector)h(\014eld)e(/)h(system)165 4405 y(if)33
b(a)h(v)m(ector)h(\014eld)e(/)h(system)g(is)f(rev)m(ersible)h
Fi(or)h Fv(Hamiltonian;)h(the)e(conserv)m(ed)g(structure)f(b)s(eing)g
(the)165 4518 y(in)m(v)m(olution)1511 4631 y(\()p Fp(x;)15
b(y)s(;)g(t)p Fv(\))26 b Fq(7!)g Fv(\()p Fq(\000)p Fp(x;)15
b(y)s(;)g Fq(\000)p Fp(t)p Fv(\))165 4798 y(or)30 b(the)h(area)g
(elemen)m(t)h(\(symplectic)g(structure\))1776 5002 y
Fp(dx)21 b Fq(^)e Fp(dy)s(;)165 5206 y Fv(resp)s(ectiv)m(ely)-8
b(.)1891 5691 y(15)p eop end
%%Page: 16 16
TeXDict begin 16 15 bop 165 337 a Fd(3.1)112 b(F)-9 b(orm)m(ulation)39
b(of)e(results)165 508 y Fv(Consider)29 b(the)i(real)g(analytic)h
(conserv)-5 b(ativ)m(e)32 b(system)1033 674 y Fp(d)p
1017 715 81 4 v 1017 798 a(dt)1122 592 y Fg( )1229 679
y Fp(x)1231 792 y(y)1323 592 y Fg(!)1414 736 y Fv(=)25
b Fp(X)1570 761 y Fc(H)1650 736 y Fv(\()p Fp(x;)15 b(y)s(;)g(t)p
Fv(\))21 b(+)f Fp(Y)g Fv(\()p Fp(x;)15 b(y)s(;)g(t)p
Fv(\))21 b(+)f Fp(Z)7 b Fv(\()p Fp(x;)15 b(y)s(;)g(t)p
Fv(\))656 b(\(3.1\))165 963 y(where)27 b(the)i(quasi-p)s(erio)s(dic)e
(v)m(ector)j(\014eld)e(on)f(the)i(righ)m(t)f(hand)f(side)h(is)g(the)g
(sum)f(of)i(the)f(Hamiltonian)165 1076 y(v)m(ector)k(\014eld)e
Fp(X)695 1102 y Fc(H)805 1076 y Fv(with)g(Hamiltonian)426
1294 y Fp(H)7 b Fv(\()p Fp(x;)15 b(y)s(;)g(t)p Fv(\))27
b(=)990 1233 y Fp(a)p Fv(\()p Fp(t)p Fv(\))p 925 1273
282 4 v 925 1357 a(2)p Fp(m)20 b Fv(+)g(2)1216 1294 y
Fp(y)1264 1257 y Fo(2)p Fn(m)p Fo(+2)1477 1294 y Fv(+)1634
1233 y Fp(b)p Fv(\()p Fp(t)p Fv(\))p 1577 1273 257 4
v 1577 1357 a(2)p Fp(n)h Fv(+)f(2)1844 1294 y Fp(x)1896
1257 y Fo(2)p Fn(n)p Fo(+2)2068 1294 y Fp(;)107 b(m;)15
b(n)25 b Fq(2)g Fh(N)2546 1308 y Fo(0)2615 1294 y Fv(with)30
b Fp(m)20 b Fv(+)g Fp(n)25 b Fq(\025)g Fv(1,)262 b(\(3.2\))165
1490 y(a)45 b(conserv)-5 b(ativ)m(e)46 b(v)m(ector)h(\014eld)d
Fp(Y)64 b Fv(that)46 b(has)e(zero)h(a)m(v)m(erage)j(and)c(a)h(conserv)
-5 b(ativ)m(e)46 b(v)m(ector)g(\014eld)f Fp(Z)165 1603
y Fv(consisting)31 b(of)g(higher)f(order)g(terms.)306
1716 y(The)j(co)s(e\016cien)m(t)j(functions)e Fp(a)g
Fv(and)f Fp(b)h Fv(in)g(\(3)p Fp(:)p Fv(2\))h(are)g(quasi-p)s(erio)s
(dic)e(functions)h(in)f Fp(t)h Fv(with)g(basic)165 1829
y(frequency)c(\012)643 1843 y Fo(1)683 1829 y Fv(.)42
b(W)-8 b(e)33 b(remark)d(that)i(the)f(v)m(ector)i(\014eld)e
Fp(X)2106 1854 y Fc(H)2217 1829 y Fv(is)g(rev)m(ersible)g(if)h(and)e
(only)h(if)g Fp(a)g Fv(and)g Fp(b)g Fv(are)165 1942 y(ev)m(en)26
b(functions)e(in)h Fp(t)p Fv(.)39 b(The)24 b(a)m(v)m(erage)k(of)d
Fp(X)1611 1967 y Fc(H)1716 1942 y Fv(coincides)h(with)f(the)h
(Hamiltonian)g(v)m(ector)h(\014eld)d(de\014ned)165 2054
y(b)m(y)30 b(a)m(v)r(\()p Fp(H)7 b Fv(\))31 b(and)f(has)g(equations)h
(of)g(motion)1440 2140 y Fg(8)1440 2215 y(>)1440 2239
y(<)1440 2389 y(>)1440 2414 y(:)1571 2224 y Fv(_)-41
b Fp(x)83 b Fv(=)126 b(a)m(v)s(\()p Fp(a)p Fv(\))p Fp(y)2146
2191 y Fo(2)p Fn(m)p Fo(+1)1572 2450 y Fv(_)-42 b Fp(y)90
b Fv(=)83 b Fq(\000)15 b Fv(a)m(v)r(\()p Fp(b)p Fv(\))p
Fp(x)2183 2417 y Fo(2)p Fn(n)p Fo(+1)2356 2450 y Fp(:)3521
2337 y Fv(\(3.3\))165 2619 y(W)-8 b(e)33 b(require)e(the)h(co)s
(e\016cien)m(ts)h(a)m(v)s(\()p Fp(a)p Fv(\))f(and)f(a)m(v)r(\()p
Fp(b)p Fv(\))i(to)f(b)s(e)f(non-zero.)45 b(In)m(tro)s(ducing)31
b(the)h(w)m(eigh)m(ts)h Fp(\013)28 b Fv(:=)224 2697 y
Fn(m)p Fo(+1)p 175 2712 251 4 v 175 2764 a Fn(m)p Fo(+)p
Fn(n)p Fo(+2)458 2732 y Fv(and)22 b Fp(\014)31 b Fv(:=)899
2697 y Fn(n)p Fo(+1)p 840 2712 V 840 2764 a Fn(m)p Fo(+)p
Fn(n)p Fo(+2)1126 2732 y Fv(=)25 b(1)5 b Fq(\000)g Fp(\013)24
b Fv(mak)m(es)g(\(3)p Fp(:)p Fv(2\))h(a)e(non-degenerate)h
(quasi-homogeneous)g(function)165 2845 y(of)30 b(degree)h
Fp(\016)f Fv(:=)25 b(2\()p Fp(n)20 b Fv(+)g(1\))p Fp(\013)27
b Fv(=)e(2\()p Fp(m)c Fv(+)f(1\))p Fp(\014)31 b(>)25
b Fv(1)31 b(\(as)f(w)m(e)h(assumed)f Fp(m)20 b Fv(+)g
Fp(n)25 b Fq(\025)g Fv(1)30 b(in)61 b(\(3)p Fp(:)p Fv(2\)\).)306
2958 y(F)-8 b(or)21 b Fp(m)26 b Fv(=)f Fp(n)f Fv(=)h(0)c(the)g(system)g
(\(3)p Fp(:)p Fv(3\))i(is)d(the)h(harmonic)g(oscillator)i(with)d
(frequency)3147 2885 y Fg(p)p 3230 2885 479 4 v 73 x
Fv(a)m(v)r(\()p Fp(a)p Fv(\))h Fq(\001)f Fv(a)m(v)r(\()p
Fp(b)p Fv(\))165 3071 y(if)30 b(b)s(oth)g(co)s(e\016cien)m(ts)i(ha)m(v)
m(e)f(the)g(same)f(sign)h(and)e(a)i(h)m(yp)s(erb)s(olic)f(linear)g
(system)h(if)f(a)m(v)r(\()p Fp(a)p Fv(\))21 b Fq(\001)f
Fv(a)m(v)s(\()p Fp(b)p Fv(\))25 b Fp(<)g Fv(0.)165 3184
y(While)45 b(our)f(results)h(remain)f(true)h(in)f(this)g(case)i(this)f
(requires)f(a)h(sligh)m(tly)h(di\013eren)m(t)f(pro)s(of)f(and)165
3297 y(since)33 b(this)g(is)g(w)m(ell-kno)m(wn)g(w)m(e)h(prefer)e(not)h
(to)g(burden)e(our)h(presen)m(tation)i(b)m(y)f(trying)g(to)g(giv)m(e)i
(case-)165 3410 y(dep)s(enden)m(t)i(form)m(ulas)h(for)g(the)h
(transformations)f(w)m(e)h(use,)h(but)e(restrict)h(from)e(the)i(outset)
g(to)g(the)165 3523 y(case)31 b Fp(m)20 b Fv(+)g Fp(n)25
b Fq(\025)g Fv(1.)41 b(Where)31 b(helpful)e(w)m(e)i(commen)m(t)h(on)e
(the)g(case)i Fp(m)25 b Fv(=)g Fp(n)g Fv(=)g(0)30 b(as)h(w)m(ell.)306
3636 y(W)-8 b(e)43 b(use)f(the)g(quasi-homogeneous)h
(gradation/\014ltration)h(de\014ned)d(b)m(y)h(the)g(w)m(eigh)m(t)i(\()p
Fp(\013;)15 b(\014)5 b Fv(\))43 b(to)165 3749 y(iden)m(tify)d(whic)m(h)
f(terms)g(are)g(of)h(higher)f(order.)67 b(F)-8 b(ollo)m(wing)41
b([1)q(])f(w)m(e)f(sa)m(y)h(that)g(a)g(v)m(ector)h(\014eld)e(is)g(of)
165 3861 y(order)32 b Fp(d)i Fv(if)f(di\013eren)m(tiation)i(in)e(the)g
(direction)h(of)f(the)g(\014eld)g(raises)h(the)f(degree)h(of)f(an)m(y)g
(function)g(b)m(y)165 3974 y(not)28 b(less)g(than)g Fp(d)p
Fv(.)40 b(Th)m(us)27 b Fp(X)1099 4000 y Fc(H)1207 3974
y Fv(is)h(of)g(order)g Fp(\016)19 b Fq(\000)c Fv(1)28
b(and)g(w)m(e)g(require)g Fp(Z)34 b Fv(in)28 b(\(3)p
Fp(:)p Fv(1\))i(to)e(ha)m(v)m(e)i(order)d(strictly)165
4087 y(larger)k(than)f Fp(\016)24 b Fq(\000)c Fv(1.)306
4200 y(In)33 b(case)h(the)g(conserv)-5 b(ativ)m(e)35
b(v)m(ector)g(\014eld)e Fp(Z)40 b Fv(is)34 b(Hamiltonian)g(this)g
(means)f(that)h(all)g(monomials)165 4313 y Fp(x)217 4280
y Fn(k)259 4313 y Fp(y)307 4280 y Fn(l)370 4313 y Fv(in)j(the)h
(Hamiltonian)g(function)f(of)h Fp(Z)43 b Fv(ha)m(v)m(e)c(degree)f
Fp(\013k)28 b Fv(+)d Fp(\014)5 b(l)39 b(>)d(\016)s Fv(.)62
b(In)37 b(the)g(rev)m(ersible)h(case)165 4426 y(this)28
b(means)g(that)g(the)g(monomials)h Fp(x)1469 4393 y Fn(i)1497
4426 y Fp(y)1545 4393 y Fn(j)1610 4426 y Fv(of)f(the)g
Fp(x)p Fv(-comp)s(onen)m(t)g(of)h Fp(Z)34 b Fv(ha)m(v)m(e)29
b(degree)g Fp(\013i)16 b Fv(+)f Fp(\014)5 b(j)32 b(>)24
b(\016)c Fq(\000)15 b Fp(\014)165 4539 y Fv(and)30 b(those)h(of)f(the)h
Fp(y)s Fv(-comp)s(onen)m(t)g(of)f Fp(Z)37 b Fv(to)32
b(ha)m(v)m(e)f(degree)g(strictly)h(larger)f(than)f Fp(\016)24
b Fq(\000)c Fp(\013)p Fv(.)42 b(The)30 b(w)m(eak)m(er)165
4652 y(prop)s(ert)m(y)36 b Fq(P)7 b Fv(\()p Fp(m)25 b
Fv(+)f(1)p Fp(;)15 b(n)25 b Fv(+)f(1\))37 b(in)f([9)q(])h(requires)f
(the)h(monomials)g(of)g(b)s(oth)e(comp)s(onen)m(ts)i(to)g(all)h(ha)m(v)
m(e)165 4765 y(degree)31 b Fp(\013i)21 b Fv(+)f Fp(\014)5
b(j)31 b(>)25 b Fv(max\()p Fp(\016)g Fq(\000)19 b Fp(\013;)c(\016)25
b Fq(\000)20 b Fp(\014)5 b Fv(\).)306 4878 y(The)30 b(quasi-p)s(erio)s
(dic)h(conserv)-5 b(ativ)m(e)33 b(v)m(ector)f(\014eld)f
Fp(Y)50 b Fv(in)31 b(\(3)p Fp(:)p Fv(1\))i(is)e(pro)s(of-generated.)42
b(P)m(art)32 b(of)f(the)165 4991 y(pro)s(cedure)k(to)i(obtain)g
(information)g(on)g(\(3)p Fp(:)p Fv(1\))h(is)e(to)i(transform)e(a)m(w)m
(a)m(y)i(the)f(time-dep)s(enden)m(t)f(part)165 5103 y(of)j
Fp(X)337 5129 y Fc(H)455 5103 y Fv(and)f(this)h(pro)s(cedure)e(turns)h
(out)g(to)i(w)m(ork)f(for)f(more)h(general)g(terms.)66
b(Hence,)41 b(the)e(main)165 5216 y(requiremen)m(t)26
b(on)f Fp(Y)46 b Fv(is)25 b(that)h(a)m(v)s(\()p Fp(Y)20
b Fv(\))26 b(=)e(0.)40 b(F)-8 b(urthermore)25 b Fp(Y)46
b Fv(has)25 b(to)i(b)s(e)e(of)g(order)g(strictly)i(larger)f(than)165
5329 y Fp(\033)31 b Fv(:=)381 5293 y Fo(1)p 381 5308
36 4 v 381 5361 a(2)426 5329 y Fv(\()p Fp(\016)26 b Fq(\000)21
b Fv(1\).)45 b(Th)m(us,)32 b(an)f(order)h(a)g(bit)g(less)g(than)f(the)h
(order)g Fp(\016)25 b Fq(\000)c Fv(1)32 b(of)g(the)g(`dominan)m(t')g
(term)g Fp(X)3628 5355 y Fc(H)165 5442 y Fv(is)e(allo)m(w)m(ed.)43
b(With)31 b(these)g(de\014nitions)e(at)j(hand)d(w)m(e)i(can)f(form)m
(ulate)i(our)e(result)g(as)g(follo)m(ws.)1891 5691 y(16)p
eop end
%%Page: 17 17
TeXDict begin 17 16 bop 165 337 a Fj(Theorem)35 b(3.1)46
b Fi(L)-5 b(et)29 b Fp(X)1001 362 y Fc(H)1094 337 y Fv(+)13
b Fp(Y)31 b Fv(+)13 b Fp(Z)35 b Fi(b)-5 b(e)29 b(a)h(quasi-p)-5
b(erio)g(dic)30 b(c)-5 b(onservative)30 b(ve)-5 b(ctor)30
b(\014eld)g(with)f(Hamilto-)165 450 y(nian)h(of)g Fp(X)535
475 y Fc(H)645 450 y Fi(given)f(by)h Fv(\(3)p Fp(:)p
Fv(2\))p Fi(,)i(a)e(c)-5 b(onservative)30 b(ve)-5 b(ctor)31
b(\014eld)f Fp(Y)50 b Fi(with)30 b(zer)-5 b(o)31 b(aver)-5
b(age)31 b(of)f(or)-5 b(der)31 b(strictly)165 562 y(lar)-5
b(ger)32 b(than)g Fp(\033)h Fi(and)f(a)f(c)-5 b(onservative)31
b(ve)-5 b(ctor)32 b(\014eld)f Fp(Z)37 b Fi(of)31 b(or)-5
b(der)32 b(strictly)g(lar)-5 b(ger)32 b(than)f Fp(\016)20
b Fq(\000)c Fv(1)p Fi(.)41 b(Assume)165 675 y(that)35
b Fv(a)m(v)r(\()p Fp(a)p Fv(\))22 b Fq(\001)g Fv(a)m(v)r(\()p
Fp(b)p Fv(\))28 b Fq(6)p Fv(=)g(0)34 b Fi(and)h(the)g(c)-5
b(ommon)36 b(fr)-5 b(e)g(quency)34 b(ve)-5 b(ctor)35
b Fv(\012)27 b(=)h(\012)2663 689 y Fo(1)2736 675 y Fi(of)34
b Fp(a;)15 b(b;)g(Y)55 b Fi(and)35 b Fp(Z)40 b Fi(satis\014es)165
788 y(the)28 b(Bruno)g(c)-5 b(ondition)29 b Fv(\(1)p
Fp(:)p Fv(4\))p Fi(.)42 b(Then)27 b(the)h(trivial)g(solution)h
Fv(\()p Fp(x)p Fv(\()p Fp(t)p Fv(\))p Fp(;)15 b(y)s Fv(\()p
Fp(t)p Fv(\)\))27 b Fq(\021)e Fv(\(0)p Fp(;)15 b Fv(0\))30
b Fi(of)d(the)h(system)g Fv(\(3)p Fp(:)p Fv(1\))165 901
y Fi(is)k(stable)i(if)e(and)i(only)f(if)f Fv(a)m(v)r(\()p
Fp(a)p Fv(\))21 b Fq(\001)g Fv(a)m(v)r(\()p Fp(b)p Fv(\))26
b Fp(>)f Fv(0)p Fi(.)165 1114 y Fv(The)36 b(pro)s(of)g(constitutes)i
(the)f(remaining)g Fq(xx)h Fv(3.2{3.4)h(b)s(elo)m(w.)60
b(F)-8 b(or)38 b(the)f(b)s(ene\014t)f(of)h(the)g(reader)g(w)m(e)165
1227 y(also)31 b(form)m(ulate)h(the)e(rev)m(ersible)h(and)f
(Hamiltonian)i(cases)f(separately)-8 b(.)165 1439 y Fj(Corollary)35
b(3.2)46 b Fi(L)-5 b(et)24 b Fp(X)1017 1465 y Fc(H)1099
1439 y Fv(+)q Fp(Y)d Fv(+)q Fp(Z)30 b Fi(b)-5 b(e)24
b(the)h(sum)f(of)g(thr)-5 b(e)g(e)25 b(r)-5 b(eversible)24
b(ve)-5 b(ctor)25 b(\014elds)g(with)f(Hamiltonian)165
1552 y(ve)-5 b(ctor)33 b(\014eld)g Fp(X)688 1577 y Fc(H)801
1552 y Fi(de\014ne)-5 b(d)34 b(by)e Fv(\(3)p Fp(:)p Fv(2\))p
Fi(,)382 1802 y Fp(Y)45 b Fv(=)25 b Fp(g)619 1816 y Fo(1)659
1802 y Fv(\()p Fp(x;)15 b(y)s(;)g(t)p Fv(\))979 1740
y Fp(@)p 952 1781 106 4 v 952 1864 a(@)5 b(x)1088 1802
y Fv(+)20 b Fp(g)1222 1816 y Fo(2)1262 1802 y Fv(\()p
Fp(x;)15 b(y)s(;)g(t)p Fv(\))1580 1740 y Fp(@)p 1555
1781 102 4 v 1555 1864 a(@)5 b(y)1853 1802 y Fi(and)187
b Fp(Z)32 b Fv(=)25 b Fp(f)2418 1816 y Fo(1)2457 1802
y Fv(\()p Fp(x;)15 b(y)s(;)g(t)p Fv(\))2777 1740 y Fp(@)p
2750 1781 106 4 v 2750 1864 a(@)5 b(x)2886 1802 y Fv(+)20
b Fp(f)3022 1816 y Fo(2)3061 1802 y Fv(\()p Fp(x;)15
b(y)s(;)g(t)p Fv(\))3379 1740 y Fp(@)p 3354 1781 102
4 v 3354 1864 a(@)5 b(y)3466 1802 y(:)165 2050 y Fi(Supp)-5
b(ose)26 b(that)f Fp(a)p Fv(\()p Fp(t)p Fv(\))g Fi(and)g
Fp(b)p Fv(\()p Fp(t)p Fv(\))f Fi(in)g Fv(\(3)p Fp(:)p
Fv(2\))i Fi(and)f Fp(g)1715 2064 y Fo(1)1755 2050 y Fv(\()p
Fp(x;)15 b(y)s(;)g(t)p Fv(\))p Fi(,)27 b Fp(g)2136 2064
y Fo(2)2176 2050 y Fv(\()p Fp(x;)15 b(y)s(;)g(t)p Fv(\))p
Fi(,)27 b Fp(f)2559 2064 y Fo(1)2598 2050 y Fv(\()p Fp(x;)15
b(y)s(;)g(t)p Fv(\))p Fi(,)26 b Fp(f)2980 2064 y Fo(2)3019
2050 y Fv(\()p Fp(x;)15 b(y)s(;)g(t)p Fv(\))25 b Fi(ar)-5
b(e)26 b(quasi-)165 2163 y(p)-5 b(erio)g(dic)36 b(in)e
Fp(t)g Fi(with)h(c)-5 b(ommon)36 b(fr)-5 b(e)g(quency)34
b(ve)-5 b(ctor)35 b Fv(\012)28 b(=)f(\012)2180 2177 y
Fo(1)2254 2163 y Fi(satisfying)34 b(the)h(Bruno)g(c)-5
b(ondition)35 b Fv(\(1)p Fp(:)p Fv(4\))p Fi(.)165 2275
y(Assume)c(furthermor)-5 b(e)34 b Fv(a)m(v)r(\()p Fp(g)1173
2289 y Fo(1)1213 2275 y Fv(\))26 b(=)f(a)m(v)r(\()p Fp(g)1540
2289 y Fo(2)1580 2275 y Fv(\))h(=)f(0)32 b Fi(and)g(that)h
Fp(g)2217 2289 y Fo(1)2289 2275 y Fi(has)f(de)-5 b(gr)g(e)g(e)33
b(strictly)g(lar)-5 b(ger)33 b(than)f Fp(\033)22 b Fv(+)c
Fp(\013)165 2388 y Fi(in)27 b Fv(\()p Fp(x;)15 b(y)s
Fv(\))p Fi(,)29 b(the)e(c)-5 b(o)g(e\016cient)28 b(function)f
Fp(g)1499 2402 y Fo(2)1566 2388 y Fi(has)h(de)-5 b(gr)g(e)g(e)28
b(strictly)g(lar)-5 b(ger)29 b(than)f Fp(\033)11 b Fv(+)d
Fp(\014)33 b Fi(and)28 b Fp(f)3184 2402 y Fo(1)3250 2388
y Fi(and)g Fp(f)3466 2402 y Fo(2)3532 2388 y Fi(have)165
2501 y(de)-5 b(gr)g(e)g(es)36 b(strictly)g(lar)-5 b(ger)36
b(than)g Fp(\016)26 b Fq(\000)c Fp(\014)35 b Fv(=)29
b(2)p Fp(\033)c Fv(+)d Fp(\013)36 b Fi(and)f Fp(\016)26
b Fq(\000)c Fp(\013)30 b Fv(=)f(2)p Fp(\033)d Fv(+)21
b Fp(\014)41 b Fi(in)35 b Fv(\()p Fp(x;)15 b(y)s Fv(\))p
Fi(,)36 b(r)-5 b(esp)g(e)g(ctively.)50 b(If)165 2614
y Fv(a)m(v)r(\()p Fp(a)p Fv(\))21 b Fq(\001)g Fv(a)m(v)r(\()p
Fp(b)p Fv(\))27 b Fq(6)p Fv(=)e(0)p Fi(,)33 b(then)h(the)f(trivial)h
(solution)g Fv(\()p Fp(x)p Fv(\()p Fp(t)p Fv(\))p Fp(;)15
b(y)s Fv(\()p Fp(t)p Fv(\)\))27 b Fq(\021)f Fv(\(0)p
Fp(;)15 b Fv(0\))35 b Fi(of)e(the)g(system)h Fv(\(3)p
Fp(:)p Fv(1\))h Fi(is)d(stable)165 2727 y(if)g(and)i(only)f(if)f
Fv(a)m(v)s(\()p Fp(a)p Fv(\))21 b Fq(\001)f Fv(a)m(v)r(\()p
Fp(b)p Fv(\))26 b Fp(>)f Fv(0)p Fi(.)165 3039 y(Pr)-5
b(o)g(of.)41 b Fv(The)25 b(conditions)g(on)g Fp(g)1219
3053 y Fo(1)1259 3039 y Fp(;)15 b(g)1342 3053 y Fo(2)1407
3039 y Fv(mak)m(e)26 b Fp(Y)44 b Fv(a)26 b(quasi-p)s(erio)s(dic)e(v)m
(ector)j(\014eld)d(of)h(order)g(strictly)g(larger)165
3152 y(than)32 b Fp(\033)k Fv(with)c(a)m(v)r(\()p Fp(Y)20
b Fv(\))30 b(=)e(0)33 b(and)f(the)h(conditions)g(on)f
Fp(f)2066 3166 y Fo(1)2105 3152 y Fp(;)15 b(f)2190 3166
y Fo(2)2262 3152 y Fv(mak)m(e)33 b Fp(Z)39 b Fv(a)33
b(quasi-p)s(erio)s(dic)f(v)m(ector)i(\014eld)165 3265
y(of)c(order)g(stricly)h(larger)g(than)f Fp(\016)25 b
Fq(\000)19 b Fv(1.)42 b(Hence,)31 b(Theorem)f(3.1)i(applies.)1005
b Fq(u)-61 b(t)165 3478 y Fj(Example)35 b(3.3)46 b Fv(F)-8
b(or)31 b Fp(m;)15 b(n)25 b Fq(\025)g Fv(1)30 b(let)i(the)e(system)1031
3595 y Fg(8)1031 3670 y(>)1031 3695 y(<)1031 3844 y(>)1031
3869 y(:)1162 3679 y Fv(_)-41 b Fp(x)25 b Fv(=)g Fp(w)1384
3693 y Fo(1)1424 3679 y Fv(\()p Fp(t)p Fv(\))p Fp(x)1579
3646 y Fo(2)p Fn(n)p Fo(+1)1772 3679 y Fv(+)20 b Fp(a)p
Fv(\()p Fp(t)p Fv(\))p Fp(y)2062 3646 y Fo(2)p Fn(m)p
Fo(+1)2274 3679 y Fv(+)g Fp(f)2410 3693 y Fo(1)2449 3679
y Fv(\()p Fp(x;)15 b(y)s(;)g(t)p Fv(\))1162 3905 y(_)-41
b Fp(y)28 b Fv(=)d Fq(\000)p Fp(b)p Fv(\()p Fp(t)p Fv(\))p
Fp(x)1580 3872 y Fo(2)p Fn(n)p Fo(+1)1773 3905 y Fv(+)20
b Fp(w)1929 3919 y Fo(2)1968 3905 y Fv(\()p Fp(t)p Fv(\))p
Fp(y)2119 3872 y Fo(2)p Fn(m)p Fo(+1)2332 3905 y Fv(+)g
Fp(f)2468 3919 y Fo(2)2507 3905 y Fv(\()p Fp(x;)15 b(y)s(;)g(t)p
Fv(\))3521 3792 y(\(3.4\))165 4106 y(ha)m(v)m(e)32 b(ev)m(en)f(quasi-p)
s(erio)s(dic)g(co)s(e\016cien)m(t)i(functions)d Fp(a;)15
b(b)31 b Fv(and)g(o)s(dd)e(quasi-p)s(erio)s(dic)i(co)s(e\016cien)m(t)i
(func-)165 4219 y(tions)h Fp(w)456 4233 y Fo(1)495 4219
y Fp(;)15 b(w)600 4233 y Fo(2)640 4219 y Fv(;)36 b(furthermore)d
Fp(f)1253 4233 y Fo(1)1292 4219 y Fv(\()p Fp(x;)15 b(y)s(;)g(t)p
Fv(\))32 b(=)e Fp(f)1753 4233 y Fo(1)1792 4219 y Fv(\()p
Fq(\000)p Fp(x;)15 b(y)s(;)g Fq(\000)p Fp(t)p Fv(\))34
b(is)g(quasi-p)s(erio)s(dic)g(in)f Fp(t)h Fv(and)f(has)g(degree)165
4332 y(strictly)25 b(larger)g(than)g Fp(\016)12 b Fq(\000)c
Fp(\014)30 b Fv(in)24 b(\()p Fp(x;)15 b(y)s Fv(\))25
b(and)f Fp(f)1692 4346 y Fo(2)1731 4332 y Fv(\()p Fp(x;)15
b(y)s(;)g(t)p Fv(\))26 b(=)f Fq(\000)p Fp(f)2252 4346
y Fo(2)2291 4332 y Fv(\()p Fq(\000)p Fp(x;)15 b(y)s(;)g
Fq(\000)p Fp(t)p Fv(\))25 b(is)f(quasi-p)s(erio)s(dic)g(in)g
Fp(t)h Fv(and)165 4445 y(has)33 b(degree)h(strictly)g(larger)g(than)e
Fp(\016)26 b Fq(\000)c Fp(\013)p Fv(.)49 b(Also,)35 b(a)m(v)r(\()p
Fp(a)p Fv(\))23 b Fq(\001)g Fv(a)m(v)r(\()p Fp(b)p Fv(\))30
b Fq(6)p Fv(=)g(0)j(and)g(the)g(common)h(frequency)165
4558 y(v)m(ector)27 b(\012)e(=)g(\012)686 4572 y Fo(1)750
4558 y Fv(of)g Fp(a;)15 b(b;)g(w)1080 4572 y Fo(1)1121
4558 y Fp(;)g(w)1226 4572 y Fo(2)1266 4558 y Fp(;)g(f)1351
4572 y Fo(1)1415 4558 y Fv(and)25 b Fp(f)1632 4572 y
Fo(2)1696 4558 y Fv(satis\014es)h(the)f(Bruno)g(condition)h(\(1)p
Fp(:)p Fv(4\).)41 b Fi(Then)28 b(the)g(trivial)165 4671
y(solution)34 b Fv(\()p Fp(x)p Fv(\()p Fp(t)p Fv(\))p
Fp(;)15 b(y)s Fv(\()p Fp(t)p Fv(\)\))27 b Fq(\021)e Fv(\(0)p
Fp(;)15 b Fv(0\))34 b Fi(of)f(the)g(system)h Fv(\(3)p
Fp(:)p Fv(4\))g Fi(is)f(stable)g(if)f(and)i(only)f(if)f
Fv(a)m(v)s(\()p Fp(a)p Fv(\))21 b Fq(\001)f Fv(a)m(v)r(\()p
Fp(b)p Fv(\))26 b Fp(>)f Fv(0)p Fi(.)306 4784 y Fv(Indeed,)35
b(the)g(quasi-p)s(erio)s(dic)f(Hamiltonian)i(v)m(ector)g(\014eld)e
Fp(X)2446 4809 y Fc(H)2560 4784 y Fv(is)h(rev)m(ersible)g(b)s(ecause)g
Fp(a)f Fv(and)g Fp(b)165 4897 y Fv(are)26 b(ev)m(en)g(functions)f(in)g
Fp(t)p Fv(.)38 b(Since)26 b Fp(w)1396 4911 y Fo(1)1461
4897 y Fv(and)e Fp(w)1697 4911 y Fo(2)1762 4897 y Fv(are)i(o)s(dd)e(in)
h Fp(t)h Fv(the)f(quasi-p)s(erio)s(dic)g(v)m(ector)i(\014eld)e
Fp(Y)45 b Fv(with)165 5010 y(co)s(e\016cien)m(t)31 b(functions)d
Fp(g)1021 5024 y Fo(1)1061 5010 y Fv(\()p Fp(x;)15 b(y)s(;)g(t)p
Fv(\))26 b(=)f Fp(w)1531 5024 y Fo(1)1571 5010 y Fv(\()p
Fp(t)p Fv(\))p Fp(x)1726 4977 y Fo(2)p Fn(n)p Fo(+1)1928
5010 y Fv(and)j Fp(g)2146 5024 y Fo(2)2186 5010 y Fv(\()p
Fp(x;)15 b(y)s(;)g(t)p Fv(\))26 b(=)f Fp(w)2656 5024
y Fo(2)2696 5010 y Fv(\()p Fp(t)p Fv(\))p Fp(y)2847 4977
y Fo(2)p Fn(m)p Fo(+1)3068 5010 y Fv(is)k(rev)m(ersible)h(and)165
5123 y(has)g(a)m(v)m(erage)j(a)m(v)r(\()p Fp(Y)20 b Fv(\))26
b(=)f(0.)41 b(The)30 b(order)g(of)g Fp(Y)51 b Fv(is)1124
5327 y Fp(\016)24 b Fq(\000)c Fv(2)15 b(max\()p Fp(\013;)g(\014)5
b Fv(\))27 b(=)e(2)15 b(min)q(\()p Fp(n\013;)g(m\014)5
b Fv(\))26 b Fp(<)f(\016)f Fq(\000)c Fv(1)1891 5691 y(17)p
eop end
%%Page: 18 18
TeXDict begin 18 17 bop 165 337 a Fv(and)30 b(strictly)h(larger)g(than)
1306 487 y Fp(\033)e Fv(=)c Fp(n\013)20 b Fv(+)1717 426
y Fp(\013)h Fq(\000)e Fp(\014)p 1717 466 226 4 v 1807
550 a Fv(2)1978 487 y(=)25 b Fp(m\014)g Fv(+)2331 426
y Fp(\014)g Fq(\000)20 b Fp(\013)p 2331 466 V 2421 550
a Fv(2)165 668 y(b)s(ecause)28 b Fp(m;)15 b(n)25 b Fq(\025)g
Fv(1.)40 b(The)28 b(conditions)g(on)g Fp(f)1691 682 y
Fo(1)1730 668 y Fp(;)15 b(f)1815 682 y Fo(2)1882 668
y Fv(mak)m(e)29 b Fp(Z)34 b Fv(a)29 b(quasi-p)s(erio)s(dic)e(rev)m
(ersible)i(v)m(ector)g(\014eld)165 781 y(of)h(order)g(strictly)i
(larger)f(than)f Fp(\016)24 b Fq(\000)c Fv(1.)41 b(Hence,)31
b(Corollary)g(3.2)h(applies.)165 981 y Fj(Remark)j(3.4)46
b Fv(The)27 b(smallness)h(condition)g(on)f Fp(f)1887
995 y Fo(1)1953 981 y Fv(and)g Fp(f)2172 995 y Fo(2)2239
981 y Fv(in)g(Corollary)h(3.2)g(\(and)g(Example)f(3.3\))i(is)165
1093 y(in)f(particular)g(satis\014ed)g(if)g Fp(f)1159
1107 y Fo(1)1198 1093 y Fp(;)15 b(f)1283 1107 y Fo(2)1348
1093 y Fv(=)25 b Fp(O)s Fv(\()p Fq(j)p Fp(x)p Fq(j)1653
1060 y Fn(n)p Fo(+1)1807 1093 y Fv(+)15 b Fq(j)p Fp(y)s
Fq(j)1991 1060 y Fn(m)p Fo(+1)2148 1093 y Fv(\))2183
1060 y Fo(2)2251 1093 y Fv(in)28 b(a)g(neigh)m(b)s(ourho)s(o)s(d)e(of)j
(\()p Fp(x;)15 b(y)s Fv(\))26 b(=)f(\(0)p Fp(;)15 b Fv(0\).)165
1293 y Fj(Corollary)35 b(3.5)46 b Fi(L)-5 b(et)26 b Fp(H)12
b Fv(+)t Fp(G)t Fv(+)t Fp(F)38 b Fi(b)-5 b(e)25 b(the)g(sum)h(of)f(the)
h(non-de)-5 b(gener)g(ate)27 b(quasi-homo)-5 b(gene)g(ous)27
b(Hamil-)165 1406 y(tonian)h Fv(\(3)p Fp(:)p Fv(2\))p
Fi(,)h(a)e(quasi-homo)-5 b(gene)g(ous)29 b(Hamiltonian)g
Fp(G)e Fi(satisfying)g Fv(a)m(v)r(\()p Fp(G)p Fv(\))g(=)e(0)i
Fi(with)g(de)-5 b(gr)g(e)g(e)28 b(strictly)165 1519 y(lar)-5
b(ger)34 b(than)f Fp(\034)j Fv(:=)836 1483 y Fo(1)p 836
1498 36 4 v 836 1550 a(2)881 1519 y Fv(\()p Fp(\016)25
b Fv(+)20 b(1\))33 b Fi(and)g(a)g(Hamiltonian)961 1710
y Fp(F)13 b Fv(\()p Fp(x;)i(y)s(;)g(t)p Fv(\))27 b(=)e
Fp(o)p Fv(\()p Fq(j)p Fp(x)p Fq(j)1619 1672 y Fn(n)p
Fo(+1)1777 1710 y Fv(+)20 b Fq(j)p Fp(y)s Fq(j)1966 1672
y Fn(m)p Fo(+1)2123 1710 y Fv(\))2158 1672 y Fo(2)2291
1710 y Fi(as)33 b Fp(x)2459 1677 y Fo(2)2519 1710 y Fv(+)20
b Fp(y)2658 1677 y Fo(2)2722 1710 y Fq(!)25 b Fv(0)p
Fi(.)165 1901 y(L)-5 b(et)29 b(furthermor)-5 b(e)31 b
Fp(a;)15 b(b;)g(G)30 b Fi(and)f Fp(F)42 b Fi(b)-5 b(e)29
b(quasi-p)-5 b(erio)g(dic)30 b(in)e Fp(t)h Fi(with)g(c)-5
b(ommon)31 b(fr)-5 b(e)g(quency)29 b(ve)-5 b(ctor)29
b Fv(\012)c(=)g(\012)3669 1915 y Fo(1)165 2013 y Fi(satisfying)36
b(the)h(Bruno)f(c)-5 b(ondition)38 b Fv(\(1)p Fp(:)p
Fv(4\))p Fi(.)53 b(Then)36 b(the)g(trivial)h(solution)g
Fv(\()p Fp(x)p Fv(\()p Fp(t)p Fv(\))p Fp(;)15 b(y)s Fv(\()p
Fp(t)p Fv(\)\))33 b Fq(\021)e Fv(\(0)p Fp(;)15 b Fv(0\))38
b Fi(of)e(the)165 2126 y(system)d(with)h(Hamiltonian)g
Fp(H)27 b Fv(+)20 b Fp(G)h Fv(+)f Fp(F)45 b Fi(is)33
b(stable)g(if)f(and)i(only)f(if)g Fv(a)m(v)r(\()p Fp(a)p
Fv(\))21 b Fq(\001)f Fv(a)m(v)r(\()p Fp(b)p Fv(\))26
b Fp(>)f Fv(0)p Fi(.)165 2423 y(Pr)-5 b(o)g(of.)63 b
Fv(The)37 b(Hamiltonian)h(v)m(ector)i(\014eld)d Fp(Y)57
b Fv(:=)37 b Fp(X)1977 2449 y Fc(G)2084 2423 y Fv(is)g(quasi-p)s(erio)s
(dic)g(with)h(a)m(v)r(\()p Fp(Y)20 b Fv(\))37 b(=)g(0)h(and)f(of)165
2536 y(order)28 b(strictly)j(larger)e(than)g Fp(\034)f
Fq(\000)17 b Fv(1)26 b(=)f Fp(\033)s Fv(.)40 b(The)29
b(Hamiltonian)h Fp(F)42 b Fv(of)30 b(the)f(quasi-p)s(erio)s(dic)g(v)m
(ector)h(\014eld)165 2649 y Fp(Z)i Fv(:=)25 b Fp(X)440
2674 y Fc(F)539 2649 y Fv(has)31 b(degree)g(strictly)g(larger)g(than)f
Fp(\016)s Fv(.)42 b(Hence,)31 b(Theorem)f(3.1)i(applies.)648
b Fq(u)-61 b(t)165 2848 y Fj(Remark)35 b(3.6)46 b Fv(Note)24
b(that)e(\(1)p Fp(:)p Fv(3\))i(and)e(\(1)p Fp(:)p Fv(2\))i(are)e(sp)s
(ecial)h(cases)g(of)f(the)g(systems)g(treated)h(in)f(Corollar-)165
2961 y(ies)h(3.2)h(and)e(3.5,)k(resp)s(ectiv)m(ely)-8
b(.)40 b(The)22 b(results)h(in)g([9])g(indicate)h(that)g(the)f(form)m
(ulation)g(of)g(Theorem)g(3.1)165 3074 y(can)31 b(still)g(b)s(e)f
(impro)m(v)m(ed,)h(for)f(instance)h(if)f Fq(\000)p Fp(ab)25
b(<)g Fv(a)m(v)r(\()p Fp(\026)p Fv(\))h Fp(<)f(ab)30
b Fv(then)1247 3313 y Fp(H)7 b Fv(\()p Fp(x;)15 b(y)s(;)g(t)p
Fv(\))26 b(=)1745 3251 y Fp(a)p 1745 3292 49 4 v 1746
3375 a Fv(4)1803 3313 y Fp(y)1851 3275 y Fo(4)1911 3313
y Fv(+)2011 3251 y Fp(\026)p Fv(\()p Fp(t)p Fv(\))p 2011
3292 159 4 v 2068 3375 a(2)2180 3313 y Fp(x)2232 3275
y Fo(2)2271 3313 y Fp(y)2319 3275 y Fo(2)2379 3313 y
Fv(+)2483 3251 y Fp(b)p 2479 3292 46 4 v 2479 3375 a
Fv(4)2535 3313 y Fp(x)2587 3275 y Fo(4)165 3525 y Fv(is)k(a)h
(de\014nite)f(homogeneous)h(Hamiltonian)h(for)e(whic)m(h)1363
3753 y Fp(Y)45 b Fv(=)25 b Fp(\026)p Fv(\()p Fp(t)p Fv(\))p
Fp(x)1767 3716 y Fo(2)1807 3753 y Fp(y)1891 3692 y(@)p
1865 3732 106 4 v 1865 3816 a(@)5 b(x)2000 3753 y Fq(\000)20
b Fp(\026)p Fv(\()p Fp(t)p Fv(\))p Fp(xy)2349 3716 y
Fo(2)2423 3692 y Fp(@)p 2399 3732 102 4 v 2399 3816 a(@)5
b(y)165 3983 y Fv(need)30 b(not)h(ha)m(v)m(e)g(zero)g(a)m(v)m(erage.)
165 4422 y Fd(3.2)112 b(Action)37 b(angle)h(v)-6 b(ariables)165
4593 y Fv(Without)30 b(loss)g(of)g(generalit)m(y)h(w)m(e)f(ma)m(y)h
(assume)e(that)h(a)m(v)r(\()p Fp(a)p Fv(\))c Fp(>)f Fv(0.)41
b(Indeed,)29 b(if)g(a)m(v)s(\()p Fp(a)p Fv(\))d Fp(<)f
Fv(0)30 b(w)m(e)g(simply)165 4706 y(rev)m(erse)i(time)g(whic)m(h)e
(leads)i(to)g(the)f(Hamiltonian)i Fq(\000)p Fp(H)7 b
Fv(\()p Fp(x;)15 b(y)s(;)g Fq(\000)p Fp(t)p Fv(\))31
b(and)g(v)m(ector)i(\014elds)d Fq(\000)p Fp(Y)20 b Fv(\()p
Fp(x;)15 b(y)s(;)g Fq(\000)p Fp(t)p Fv(\),)165 4819 y
Fq(\000)p Fp(Z)7 b Fv(\()p Fp(x;)15 b(y)s(;)g Fq(\000)p
Fp(t)p Fv(\))30 b(still)i(satisfying)f(the)f(conditions)h(of)g(Theorem)
f(3.1.)306 4932 y(F)-8 b(or)30 b(a)m(v)r(\()p Fp(b)p
Fv(\))c Fp(>)f Fv(0)k(all)h(orbits)f(of)g(the)h(autonomous)f(planar)g
(system)g(\(3)p Fp(:)p Fv(3\))i(are)e(p)s(erio)s(dic.)40
b(Denoting)165 5045 y(b)m(y)30 b(\()p Fp(S)5 b Fv(\()p
Fp(t)p Fv(\))p Fp(;)15 b(C)7 b Fv(\()p Fp(t)p Fv(\)\))32
b(the)f(solution)g(of)g(\(3)p Fp(:)p Fv(3\))h(with)e(initial)i
(conditions)f Fp(S)5 b Fv(\(0\))26 b(=)g(0)k(and)g Fp(C)7
b Fv(\(0\))26 b(=)f(1)31 b(and)f(b)m(y)165 5158 y Fp(T)218
5172 y Fo(0)283 5158 y Fp(>)25 b Fv(0)30 b(the)h(minimal)f(p)s(erio)s
(d)g(w)m(e)g(de\014ne)g(the)h(transformation)1432 5341
y(\010)25 b(:)84 b Fh(R)1692 5308 y Fo(+)1771 5341 y
Fq(\002)20 b Fh(T)83 b Fq(\000)-15 b(!)138 b Fh(R)2345
5308 y Fo(2)1666 5454 y Fv(\()p Fp(\032;)15 b(')p Fv(\))146
b Fq(7!)111 b Fv(\()p Fp(x;)15 b(y)s Fv(\))3521 5398
y(\(3.5\))1891 5691 y(18)p eop end
%%Page: 19 19
TeXDict begin 19 18 bop 165 337 a Fv(b)m(y)48 b(means)g(of)g
Fp(x)55 b Fv(=)g Fp(c)998 304 y Fn(\013)1048 337 y Fp(\032)1095
304 y Fn(\013)1144 337 y Fp(S)5 b Fv(\()p Fp('T)1352
351 y Fo(0)1393 337 y Fv(\))48 b(and)g Fp(y)57 b Fv(=)e
Fp(c)1938 304 y Fn(\014)1986 337 y Fp(\032)2033 304 y
Fn(\014)2080 337 y Fp(C)7 b Fv(\()p Fp('T)2299 351 y
Fo(0)2339 337 y Fv(\))48 b(where)g Fp(c)55 b Fv(=)3027
301 y Fn(m)p Fo(+)p Fn(n)p Fo(+2)p 2933 316 440 4 v 2933
369 a(\()p Fn(n)p Fo(+1\))12 b(a)n(v)r(\()p Fn(a)p Fo(\))p
Fn(T)3336 378 y Fm(0)3382 337 y Fv(.)94 b(Since)165 462
y(\()p Fp(S)5 b Fv(\()p Fq(\000)p Fp(t)p Fv(\))p Fp(;)15
b(C)7 b Fv(\()p Fq(\000)p Fp(t)p Fv(\)\))50 b(=)f(\()p
Fq(\000)p Fp(S)5 b Fv(\()p Fp(t)p Fv(\))p Fp(;)15 b(C)7
b Fv(\()p Fp(t)p Fv(\)\))46 b(this)e(transformation)h(is)g(equiv)-5
b(arian)m(t)46 b(with)e(resp)s(ect)h(to)g(the)165 575
y(in)m(v)m(olutions)31 b(\()p Fp(\032;)15 b(')p Fv(\))27
b Fq(7!)e Fv(\()p Fp(\032;)15 b Fq(\000)p Fp(')p Fv(\))32
b(and)e(\()p Fp(x;)15 b(y)s Fv(\))26 b Fq(7!)f Fv(\()p
Fq(\000)p Fp(x;)15 b(y)s Fv(\),)31 b(and)f(b)s(ecause)789
761 y(a)m(v)r(\()p Fp(a)p Fv(\))p 754 801 282 4 v 754
885 a(2)p Fp(m)20 b Fv(+)g(2)1046 822 y Fp(C)1118 785
y Fo(2)p Fn(m)p Fo(+2)1309 822 y Fv(\()p Fp(t)p Fv(\))h(+)1561
761 y(a)m(v)r(\()p Fp(b)p Fv(\))p 1534 801 257 4 v 1534
885 a(2)p Fp(n)f Fv(+)g(2)1800 822 y Fp(S)1861 785 y
Fo(2)p Fn(n)p Fo(+2)2034 822 y Fv(\()p Fp(t)p Fv(\))25
b(=)g(a)m(v)s(\()p Fp(H)7 b Fv(\)\(0)p Fp(;)15 b Fv(1\))27
b(=)2873 761 y(a)m(v)r(\()p Fp(a)p Fv(\))p 2837 801 282
4 v 2837 885 a(2)p Fp(m)21 b Fv(+)f(2)165 1055 y(the)30
b(mapping)g(\010)g(is)h(area-preserving)g(\(i.e.)g(canonical)h(or)f
(symplectic\).)42 b(In)30 b(fact,)175 1181 y Fg(\014)175
1230 y(\014)175 1280 y(\014)175 1330 y(\014)216 1241
y Fp(@)5 b Fv(\()p Fp(x;)15 b(y)s Fv(\))p 212 1282 271
4 v 212 1365 a Fp(@)5 b Fv(\()p Fp(\032;)15 b(')p Fv(\))493
1181 y Fg(\014)493 1230 y(\014)493 1280 y(\014)493 1330
y(\014)604 1303 y Fv(=)758 1206 y Fg(\014)758 1255 y(\014)758
1305 y(\014)785 1303 y Fp(\013T)896 1317 y Fo(0)952 1303
y Fv(a)m(v)r(\()p Fp(b)p Fv(\))p Fp(c)1192 1265 y Fn(\013)p
Fo(+)p Fn(\014)1340 1303 y Fp(\032)1387 1265 y Fn(\013)p
Fo(+)p Fn(\014)s Fx(\000)p Fo(1)1625 1303 y Fp(S)1686
1265 y Fo(2)p Fn(n)p Fo(+2)1858 1303 y Fv(\()p Fp('T)2005
1317 y Fo(0)2046 1303 y Fv(\))20 b(+)g Fp(\014)5 b(T)2301
1317 y Fo(0)2356 1303 y Fv(a)m(v)r(\()p Fp(a)p Fv(\))p
Fp(c)2605 1265 y Fn(\013)p Fo(+)p Fn(\014)2754 1303 y
Fp(\032)2801 1265 y Fn(\013)p Fo(+)p Fn(\014)s Fx(\000)p
Fo(1)3038 1303 y Fp(C)3110 1265 y Fo(2)p Fn(m)p Fo(+2)3302
1303 y Fv(\()p Fp('T)3449 1317 y Fo(0)3489 1303 y Fv(\))3524
1206 y Fg(\014)3524 1255 y(\014)3524 1305 y(\014)604
1541 y Fv(=)946 1480 y(1)p 768 1520 403 4 v 768 1604
a Fp(m)20 b Fv(+)g Fp(n)f Fv(+)h(2)1200 1541 y Fq(\001)1245
1444 y Fg(\014)1245 1494 y(\014)1245 1544 y(\014)1273
1541 y Fp(T)1326 1555 y Fo(0)1366 1541 y Fp(c)g Fq(\001)1471
1447 y Fg(\020)1520 1541 y Fv(\()p Fp(m)h Fv(+)e(1\))c(a)m(v)t(\()p
Fp(b)p Fv(\))p Fp(S)2105 1504 y Fo(2)p Fn(n)p Fo(+2)2278
1541 y Fv(\()p Fp('T)2425 1555 y Fo(0)2465 1541 y Fv(\))21
b(+)f(\()p Fp(n)g Fv(+)g(1\))15 b(a)m(v)s(\()p Fp(a)p
Fv(\))p Fp(C)3191 1504 y Fo(2)p Fn(m)p Fo(+2)3383 1541
y Fv(\()p Fp('T)3530 1555 y Fo(0)3570 1541 y Fv(\))3605
1447 y Fg(\021)3655 1444 y(\014)3655 1494 y(\014)3655
1544 y(\014)604 1703 y Fv(=)83 b(1)p Fp(:)165 1903 y
Fv(Hence,)24 b(\010)e(transforms)e(conserv)-5 b(ativ)m(e)24
b(v)m(ector)f(\014elds)f(in)m(to)g(conserv)-5 b(ativ)m(e)24
b(v)m(ector)f(\014elds.)38 b(In)21 b(particular,)165
2016 y(the)30 b(system)h(\(3)p Fp(:)p Fv(3\))h(is)f(transformed)e(in)m
(to)1532 2258 y(_)-43 b Fp(\032)83 b Fv(=)f Fq(\000)1878
2197 y Fp(@)5 b(h)1983 2211 y Fo(0)p 1878 2237 146 4
v 1894 2321 a Fp(@)g(')2058 2258 y Fv(=)25 b(0)1526 2496
y(_)-50 b Fp(')84 b Fv(=)1807 2435 y Fp(@)5 b(h)1912
2449 y Fo(0)p 1807 2475 V 1830 2558 a Fp(@)g(\032)1988
2496 y Fv(=)25 b Fp(d)20 b Fq(\001)h Fp(\032)2244 2459
y Fn(\016)r Fx(\000)p Fo(1)165 2734 y Fv(with)30 b(Hamiltonian)1146
2883 y Fp(h)1198 2897 y Fo(0)1238 2883 y Fv(\()p Fp(\032;)15
b(';)g(t)p Fv(\))27 b(=)e Fp(h)1702 2897 y Fo(0)1741
2883 y Fv(\()p Fp(\032)p Fv(\))h(=)1990 2822 y Fp(c)2029
2789 y Fn(\016)2083 2822 y Fv(a)m(v)r(\()p Fp(a)p Fv(\))p
1990 2862 304 4 v 2001 2946 a(2)p Fp(m)20 b Fv(+)g(2)2303
2883 y Fp(\032)2350 2846 y Fn(\016)2414 2883 y Fv(=)2520
2822 y Fp(d)g Fq(\001)g Fp(\032)2679 2789 y Fn(\016)p
2520 2862 198 4 v 2597 2946 a Fp(\016)165 3092 y Fv(where)30
b(w)m(e)h(write)f Fp(d)c Fv(=)f Fp(\014)5 b(c)1058 3059
y Fn(\016)1101 3092 y Fv(a)m(v)r(\()p Fp(a)p Fv(\).)42
b(The)30 b(original)h(v)m(ector)h(\014eld)e Fp(X)2423
3118 y Fc(H)2523 3092 y Fv(+)20 b Fp(Y)40 b Fv(+)20 b
Fp(Z)37 b Fv(is)31 b(transformed)e(in)m(to)1530 3292
y Fp(X)1590 3318 y Ft(\010)1650 3288 y Fb(\003)1689 3318
y Fc(H)1789 3292 y Fv(+)20 b(\010)1946 3255 y Fx(\003)1985
3292 y Fp(Y)40 b Fv(+)20 b(\010)2235 3255 y Fx(\003)2274
3292 y Fp(Z)1185 b Fv(\(3.6\))165 3492 y(with)1257 3605
y Fp(H)7 b Fv(\(\010\()p Fp(\032;)15 b(')p Fv(\))p Fp(;)g(t)p
Fv(\))27 b(=)e Fp(h)1940 3619 y Fo(0)1980 3605 y Fv(\()p
Fp(\032)p Fv(\))c(+)f Fp(h)2261 3619 y Fo(1)2300 3605
y Fv(\()p Fp(\032;)15 b(';)g(t)p Fv(\))p Fp(:)165 3769
y Fv(Here)736 3907 y Fp(h)788 3921 y Fo(1)828 3907 y
Fv(\()p Fp(\032;)g(';)g(t)p Fv(\))27 b(=)e Fp(c)1279
3870 y Fn(\016)1317 3907 y Fp(\032)1364 3870 y Fn(\016)1417
3788 y Fg(\024)1517 3846 y Fp(a)1565 3860 y Fo(1)1604
3846 y Fv(\()p Fp(t)p Fv(\))p 1471 3886 282 4 v 1471
3970 a(2)p Fp(m)c Fv(+)e(2)1763 3907 y Fp(C)1835 3870
y Fo(2)p Fn(m)p Fo(+2)2026 3907 y Fv(\()p Fp('T)2173
3921 y Fo(0)2214 3907 y Fv(\))h(+)2408 3846 y Fp(b)2447
3860 y Fo(1)2486 3846 y Fv(\()p Fp(t)p Fv(\))p 2370 3886
257 4 v 2370 3970 a(2)p Fp(n)g Fv(+)g(2)2637 3907 y Fp(S)2698
3870 y Fo(2)p Fn(n)p Fo(+2)2870 3907 y Fv(\()p Fp('T)3017
3921 y Fo(0)3058 3907 y Fv(\))3093 3788 y Fg(\025)3521
3907 y Fv(\(3.7\))165 4107 y(where)30 b(w)m(e)h(ha)m(v)m(e)g(split)1099
4307 y Fp(a)p Fv(\()p Fp(t)p Fv(\))25 b(=)g(a)m(v)s(\()p
Fp(a)p Fv(\))20 b(+)g Fp(a)1741 4321 y Fo(1)1781 4307
y Fv(\()p Fp(t)p Fv(\))p Fp(;)107 b(b)p Fv(\()p Fp(t)p
Fv(\))26 b(=)e(a)m(v)s(\()p Fp(b)p Fv(\))d(+)e Fp(b)2631
4321 y Fo(1)2671 4307 y Fv(\()p Fp(t)p Fv(\))165 4507
y(in)m(to)31 b(the)g(constan)m(t)g(a)m(v)m(erages)i(and)d(the)h
(time-dep)s(enden)m(t)f(parts)g(with)g(a)m(v)m(erages)1446
4707 y(a)m(v)r(\()p Fp(a)1621 4721 y Fo(1)1661 4707 y
Fv(\))25 b(=)g(0)p Fp(;)107 b Fv(a)m(v)r(\()p Fp(b)2160
4721 y Fo(1)2200 4707 y Fv(\))26 b(=)f(0)p Fp(:)165 4906
y Fv(F)-8 b(urthermore)1089 5039 y(\010)1155 5002 y Fx(\003)1194
5039 y Fp(Y)20 b Fv(\()p Fp(\032;)15 b(';)g(t)p Fv(\))28
b(=)d Fp(\030)1720 5053 y Fo(1)1759 5039 y Fv(\()p Fp(\032;)15
b(';)g(t)p Fv(\))2083 4978 y Fp(@)p 2058 5018 101 4 v
2058 5102 a(@)5 b(\032)2190 5039 y Fv(+)20 b Fp(\030)2321
5053 y Fo(2)2360 5039 y Fv(\()p Fp(\032;)15 b(';)g(t)p
Fv(\))2691 4978 y Fp(@)p 2659 5018 113 4 v 2659 5102
a(@)5 b(')165 5242 y Fv(where)30 b(the)g(co)s(e\016cien)m(t)j
(functions)c Fp(\030)1440 5256 y Fn(i)1499 5242 y Fv(are)h(b)s(oth)g
(quasi-p)s(erio)s(dic)g(in)g Fp(t)g Fv(with)g(zero)i(a)m(v)m(erage)h
(and)1200 5442 y Fp(\030)1240 5456 y Fo(1)1304 5442 y
Fv(=)25 b Fp(o)p Fv(\()p Fp(\032)1526 5405 y Fn(\034)1570
5442 y Fv(\))p Fp(;)107 b(\030)1777 5456 y Fo(2)1841
5442 y Fv(=)25 b Fp(o)p Fv(\()p Fp(\032)2063 5405 y Fn(\033)2110
5442 y Fv(\))183 b(as)30 b Fp(\032)25 b Fq(!)h Fv(0)1891
5691 y(19)p eop end
%%Page: 20 20
TeXDict begin 20 19 bop 165 337 a Fv(since)30 b Fp(Y)50
b Fv(is)30 b(of)g(order)f(strictly)i(larger)f(than)g
Fp(\034)f Fq(\000)19 b Fv(1)26 b(=)f Fp(\033)s Fv(.)40
b(In)29 b(other)h(w)m(ords,)g Fp(Y)50 b Fv(is)30 b(of)g(order)f
Fp(\033)22 b Fv(+)d Fp(\027)36 b Fv(and)165 450 y(w)m(e)31
b(ha)m(v)m(e)1342 562 y Fp(\030)1382 576 y Fo(1)1446
562 y Fv(=)25 b Fp(O)s Fv(\()p Fp(\032)1696 525 y Fn(\034)8
b Fo(+)p Fn(\027)1834 562 y Fv(\))p Fp(;)106 b(\030)2040
576 y Fo(2)2105 562 y Fv(=)25 b Fp(O)s Fv(\()p Fp(\032)2355
525 y Fn(\033)r Fo(+)p Fn(\027)2496 562 y Fv(\))165 718
y(for)i(su\016cien)m(tly)h(small)g Fp(\027)j(>)25 b Fv(0.)40
b(Since)28 b Fp(Z)34 b Fv(is)27 b(of)h(order)f(strictly)h(larger)g
(than)g Fp(\016)18 b Fq(\000)c Fv(1)26 b(=)f(2)p Fp(\033)31
b Fv(w)m(e)c(similarly)165 831 y(obtain)1106 964 y(\010)1172
926 y Fx(\003)1211 964 y Fp(Z)7 b Fv(\()p Fp(\032;)15
b(';)g(t)p Fv(\))26 b(=)f Fp(O)s Fv(\()p Fp(\032)1845
926 y Fn(\016)r Fo(+)p Fn(\027)1977 964 y Fv(\))2046
902 y Fp(@)p 2022 943 101 4 v 2022 1026 a(@)5 b(\032)2153
964 y Fv(+)20 b Fp(O)s Fv(\()p Fp(\032)2398 926 y Fo(2)p
Fn(\033)r Fo(+)p Fn(\027)2574 964 y Fv(\))2649 902 y
Fp(@)p 2619 943 113 4 v 2619 1026 a(@)5 b(')2742 964
y(;)165 1158 y Fv(shrinking)29 b Fp(\027)36 b Fv(a)31
b(bit)f(if)h(necessary)f(to)h(ensure)f(that)h Fp(Z)37
b Fv(is)30 b(of)h(order)f(2)p Fp(\033)24 b Fv(+)19 b
Fp(\027)6 b Fv(.)165 1348 y Fj(Remark)35 b(3.7)46 b Fv(F)-8
b(or)26 b Fp(m)f Fv(=)g Fp(n)g Fv(=)f(0)i(the)e(transformation)h(\010)g
(is)f(de\014ned)g(in)g(terms)h(of)f Fp(S)5 b Fv(\()p
Fp(t)p Fv(\))26 b(=)f(sin)15 b Fp(\024t)25 b Fv(and)165
1461 y Fp(C)7 b Fv(\()p Fp(t)p Fv(\))25 b(=)g(cos)16
b Fp(\024t)30 b Fv(where)g Fp(\024)c Fv(=)1150 1388 y
Fg(p)p 1233 1388 479 4 v 73 x Fv(a)m(v)r(\()p Fp(a)p
Fv(\))21 b Fq(\001)g Fv(a)m(v)r(\()p Fp(b)p Fv(\))31
b(is)f(the)h(frequency)f(of)g(the)h(harmonic)f(oscillator)j(\(3)p
Fp(:)p Fv(3\).)165 1891 y Fd(3.3)112 b(Dynamical)39 b(stabilit)m(y)165
2063 y Fv(The)30 b(transformed)f(v)m(ector)j(\014eld)e(\(3)p
Fp(:)p Fv(6\))i(has)f(equations)g(of)f(motion)1191 2242
y(_)-43 b Fp(\032)83 b Fv(=)g Fp(\021)1502 2256 y Fo(1)1541
2242 y Fv(\()p Fp(\032;)15 b(';)g(t)p Fv(\))22 b(+)e
Fp(\020)1983 2256 y Fo(1)2023 2242 y Fv(\()p Fp(\032;)15
b(';)g(t)p Fv(\))1185 2380 y(_)-49 b Fp(')83 b Fv(=)g
Fp(d)20 b Fq(\001)h Fp(\032)1617 2347 y Fn(\016)r Fx(\000)p
Fo(1)1765 2380 y Fv(+)f Fp(\021)1901 2394 y Fo(2)1940
2380 y Fv(\()p Fp(\032;)15 b(';)g(t)p Fv(\))23 b(+)c
Fp(\020)2382 2394 y Fo(2)2422 2380 y Fv(\()p Fp(\032;)c(';)g(t)p
Fv(\))3521 2311 y(\(3.8\))165 2554 y(with)30 b(expressions)g(at)h(the)g
(righ)m(t)g(hand)e(side)h(de\014ned)f(b)m(y)1312 2774
y Fp(X)1372 2800 y Fc(h)1420 2812 y Fa(1)1482 2774 y
Fv(+)20 b(\010)1639 2736 y Fx(\003)1678 2774 y Fp(Y)103
b Fv(=:)83 b Fp(\021)2058 2788 y Fo(1)2131 2712 y Fp(@)p
2107 2752 101 4 v 2107 2836 a(@)5 b(\032)2238 2774 y
Fv(+)20 b Fp(\021)2374 2788 y Fo(2)2453 2712 y Fp(@)p
2423 2752 113 4 v 2423 2836 a(@)5 b(')1577 3011 y Fv(\010)1643
2974 y Fx(\003)1682 3011 y Fp(Z)90 b Fv(=:)83 b Fp(\020)2053
3025 y Fo(1)2126 2950 y Fp(@)p 2102 2990 101 4 v 2102
3074 a(@)5 b(\032)2233 3011 y Fv(+)19 b Fp(\020)2363
3025 y Fo(2)2442 2950 y Fp(@)p 2413 2990 113 4 v 2413
3074 a(@)5 b(')2535 3011 y(:)165 3232 y Fv(The)27 b(co)s(e\016cien)m(t)
j(functions)d Fp(\021)1205 3246 y Fo(1)1272 3232 y Fv(and)h
Fp(\021)1492 3246 y Fo(2)1559 3232 y Fv(ha)m(v)m(e)h(zero)g(a)m(v)m
(erage)h(in)d Fp(t)p Fv(.)40 b(This)27 b(implies)h(that)g(the)g
(inde\014nite)165 3345 y(in)m(tegrals)1211 3371 y Fg(Z)1309
3486 y Fp(\021)1354 3500 y Fo(1)1394 3486 y Fv(\()p Fp(\032;)15
b(';)g(t)p Fv(\))p Fp(dt)93 b Fv(and)2108 3371 y Fg(Z)2206
3486 y Fp(\021)2251 3500 y Fo(2)2291 3486 y Fv(\()p Fp(\032;)15
b(';)g(t)p Fv(\))p Fp(dt)165 3670 y Fv(are)35 b(again)g(quasi-p)s(erio)
s(dic)f(and)g(can)h(b)s(e)f(used)f(to)j(de\014ne)d(a)i(time-dep)s
(enden)m(t)g(transformation)g(\011)3654 3684 y Fn(t)3683
3670 y Fv(.)165 3782 y(T)-8 b(o)33 b(ensure)g(that)g(the)g(transformed)
g(system)g(is)g(again)h(conserv)-5 b(ativ)m(e)35 b(w)m(e)e(de\014ne)g
(\011)3090 3796 y Fn(t)3152 3782 y Fv(as)g(the)g(time-1-)165
3895 y(mapping)d(of)g(the)h(`auxiliary')g(v)m(ector)h(\014eld)e
Fp(W)38 b Fv(=)25 b Fq(\000)p Fp(X)2049 3922 y Fc(h)2097
3934 y Fa(1)2158 3895 y Fq(\000)20 b Fv(\010)2315 3862
y Fx(\003)2354 3895 y Fp(Y)g Fv(.)41 b(The)30 b(transformation)1197
4077 y(\()p Fp(\045;)15 b(#)p Fv(\))26 b(=)f(\011)1601
4091 y Fn(t)1630 4077 y Fv(\()p Fp(\032;)15 b(')p Fv(\))27
b(=:)e(\()p Fp(\032;)15 b(')p Fv(\))22 b(+)e Fp( )s Fv(\()p
Fp(\032;)15 b(';)g(t)p Fv(\))165 4259 y(with)1470 4336
y Fp(@)5 b( )s Fv(\()p Fp(\032;)15 b(';)g(t)p Fv(\))p
1470 4376 407 4 v 1631 4459 a Fp(@)5 b(t)1912 4397 y
Fv(=)25 b Fq(\000)p Fp(\021)s Fv(\()p Fp(\045;)15 b(#;)g(t)p
Fv(\))165 4579 y(turns)29 b(\(3)p Fp(:)p Fv(8\))j(in)m(to)627
4765 y(_)-44 b Fp(\045)83 b Fv(=)g Fp(\021)937 4779 y
Fo(1)997 4765 y Fv(+)20 b Fp(\020)1128 4779 y Fo(1)1187
4765 y Fv(+)1288 4725 y Fn(@)t( )1375 4734 y Fm(1)p 1288
4744 122 4 v 1310 4797 a Fn(@)t(\032)1438 4765 y Fv(_)-43
b Fp(\032)20 b Fv(+)1588 4725 y Fn(@)t( )1675 4734 y
Fm(1)p 1588 4744 V 1605 4797 a Fn(@)t(')1744 4765 y Fv(_)-49
b Fp(')20 b Fv(+)1900 4725 y Fn(@)t( )1987 4734 y Fm(1)p
1900 4744 V 1928 4797 a Fn(@)t(t)2057 4765 y Fv(=)25
b Fp(O)s Fv(\()p Fp(\045)2307 4732 y Fn(\016)r Fo(+)p
Fn(\027)2439 4765 y Fv(\))624 4887 y(_)602 4911 y Fp(#)82
b Fv(=)h Fp(d)21 b Fq(\001)f Fp(\045)1052 4878 y Fn(\016)r
Fx(\000)p Fo(1)1200 4911 y Fv(+)g Fp(\021)1336 4925 y
Fo(2)1396 4911 y Fv(+)g Fp(\020)1527 4925 y Fo(2)1586
4911 y Fv(+)1687 4870 y Fn(@)t( )1774 4879 y Fm(2)p 1687
4890 V 1710 4942 a Fn(@)t(\032)1838 4911 y Fv(_)-44 b
Fp(\032)20 b Fv(+)1987 4870 y Fn(@)t( )2074 4879 y Fm(2)p
1987 4890 V 2005 4942 a Fn(@)t(')2144 4911 y Fv(_)-50
b Fp(')21 b Fv(+)2299 4870 y Fn(@)t( )2386 4879 y Fm(2)p
2299 4890 V 2327 4942 a Fn(@)t(t)2456 4911 y Fv(=)k Fp(d)c
Fq(\001)f Fp(\045)2712 4878 y Fo(2)p Fn(\033)2815 4911
y Fv(+)g Fp(O)s Fv(\()p Fp(\045)3060 4878 y Fo(2)p Fn(\033)r
Fo(+)p Fn(\027)3236 4911 y Fv(\))3521 4840 y(\(3.9\))165
5096 y(and)29 b(w)m(e)g(can)h(apply)f(the)g(results)g(from)g(Section)h
(2.)41 b(T)-8 b(o)30 b(this)f(end)g(w)m(e)g(expand)g(around)f(a)i
(\014xed)f(small)165 5209 y(v)-5 b(alue)31 b Fp(\045)25
b Fv(=)g Fp(r)s(")30 b Fv(with)g Fp(r)e Fq(2)d Fv([)1081
5173 y Fo(1)p 1081 5188 36 4 v 1081 5240 a(2)1126 5209
y Fp(;)1177 5173 y Fo(3)p 1177 5188 V 1177 5240 a(2)1222
5209 y Fv(])31 b(and)e(scale)j(the)f(translated)g(v)-5
b(ariable)31 b(b)m(y)f Fp(")2768 5176 y Fn(\024)2844
5209 y Fv(with)1704 5418 y Fp(\024)c Fv(=)1985 5356 y
Fp(\027)p 1888 5397 246 4 v 1888 5480 a Fv(2)p Fp(\016)e
Fq(\000)c Fv(1)2144 5418 y Fp(;)1891 5691 y Fv(20)p eop
end
%%Page: 21 21
TeXDict begin 21 20 bop 165 337 a Fv(cf.)31 b([2].)41
b(This)30 b(amoun)m(ts)g(for)h(ev)m(ery)g(0)25 b Fp(<)g(")h(<)f(")1776
304 y Fx(\003)1846 337 y Fv(to)31 b(the)g(transformation)1275
537 y(\002)1346 551 y Fn(")1408 537 y Fv(:)1516 468 y
Fg(\000)1564 502 y Fx(\000)p Fn(r)p 1564 517 89 4 v 1572
569 a(")1605 550 y Ff(\024)1662 537 y Fp(;)1732 502 y
Fn(r)p 1713 517 73 4 v 1713 569 a(")1746 550 y Ff(\024)1796
468 y Fg(\001)1854 537 y Fq(\002)20 b Fh(T)83 b Fq(\000)-15
b(!)83 b Fh(R)2373 504 y Fo(+)2452 537 y Fq(\002)20 b
Fh(T)1656 675 y Fv(\()p Fp(I)7 b(;)15 b(\022)s Fv(\))252
b Fq(7!)148 b Fv(\()p Fp(\045;)15 b(#)p Fv(\))165 876
y(de\014ned)29 b(b)m(y)h Fp(\045)c Fv(=)e Fp(")p Fv(\()p
Fp(r)g Fv(+)c Fp(")1047 843 y Fn(\024)1092 876 y Fp(I)7
b Fv(\),)31 b Fp(#)25 b Fv(=)g Fp(\022)33 b Fv(and)c(turns)g(\(3)p
Fp(:)p Fv(9\))k(in)m(to)1260 1057 y(_)1239 1080 y Fp(I)90
b Fv(=)83 b Fp(O)s Fv(\()p Fp(")1672 1042 y Fn(\016)r
Fo(+)p Fn(\027)t Fx(\000)p Fo(1)p Fx(\000)p Fn(\024)1990
1080 y Fv(\))25 b(=)g Fp(O)s Fv(\()p Fp(")2295 1042 y
Fo(2)p Fn(\033)r Fo(\(1+2)p Fn(\024)p Fo(\))2599 1080
y Fv(\))1258 1194 y(_)1241 1218 y Fp(\022)85 b Fv(=)e
Fp(dr)1614 1180 y Fo(2)p Fn(\033)1696 1218 y Fp(")1738
1180 y Fo(2)p Fn(\033)1840 1218 y Fv(+)20 b Fp(O)s Fv(\()p
Fp(")2080 1180 y Fo(2)p Fn(\033)r Fo(\(1+)p Fn(\024)p
Fo(\))2349 1218 y Fv(\))p Fp(:)165 1421 y Fv(Rescaling)32
b(time)f(b)m(y)f Fp(")946 1388 y Fo(2)p Fn(\033)1059
1421 y Fv(then)g(yields)1572 1602 y(_)1551 1625 y Fp(I)90
b Fv(=)83 b Fp(O)s Fv(\()p Fp(")1984 1587 y Fo(4)p Fn(\033)r(\024)2107
1625 y Fv(\))1570 1739 y(_)1553 1763 y Fp(\022)i Fv(=)e
Fp(A)20 b Fv(+)g Fp(O)s Fv(\()p Fp(")2163 1725 y Fo(2)p
Fn(\033)r(\024)2287 1763 y Fv(\))165 1966 y(in)30 b(the)g(form)g(\(2)p
Fp(:)p Fv(1\))j(or)d(\(2)p Fp(:)p Fv(26\))j(with)d(parameter)1020
2227 y Fp(A)c Fv(=)e Fp(dr)1300 2189 y Fo(2)p Fn(\033)1408
2227 y Fv(=)1543 2165 y(1)p 1514 2206 104 4 v 1514 2293
a Fp(T)1580 2262 y Fn(\016)1567 2318 y Fo(0)1642 2108
y Fg(\022)1833 2165 y Fp(r)p 1713 2206 283 4 v 1713 2289
a(\014)d Fv(a)m(v)r(\()p Fp(a)p Fv(\))2006 2108 y Fg(\023)2067
2131 y Fo(2)p Fn(\033)2174 2227 y Fq(2)k Fh(R)p Fp(;)106
b(r)28 b Fq(2)d Fv([)2641 2165 y(1)p 2641 2206 46 4 v
2641 2289 a(2)2697 2227 y Fp(;)2747 2165 y Fv(3)p 2747
2206 V 2747 2289 a(2)2802 2227 y(])p Fp(:)165 2493 y
Fv(Here)42 b(w)m(e)g(can)f(c)m(ho)s(ose)i Fp(s)g Fv(=)g
Fp(")1255 2460 y Fn(\033)r(\024)1385 2493 y Fv(to)f(apply)f(Theorems)g
(2.1)h(and)f(2.3,)k(then)d Fp(s)2991 2460 y Fo(2)3073
2493 y Fv(=)i Fp(")3230 2460 y Fo(2)p Fn(\033)r(\024)3394
2493 y Fv(and)d(the)165 2606 y(righ)m(t)31 b(hand)f(sides)h(ful\014ll)g
(\(2)p Fp(:)p Fv(2\))h(or)f(\(2)p Fp(:)p Fv(27\),)j(resp)s(ectiv)m(ely)
-8 b(.)44 b(The)31 b(resulting)g(quasi-p)s(erio)s(dic)g(solutions)165
2719 y(determine)21 b(in)m(v)-5 b(arian)m(t)22 b(cylinders)e(around)g
(the)h Fp(t)p Fv(-axis,)i(con\014ning)d(in)m(tegral)j(curv)m(es)e(and)f
(th)m(us)g(implying)165 2832 y(stabilit)m(y)32 b(of)e(the)h(orbit)f
(along)i(the)e Fp(t)p Fv(-axis.)165 3044 y Fj(Remark)35
b(3.8)46 b Fv(F)-8 b(or)34 b Fp(m)c Fv(=)g Fp(n)f Fv(=)h(0)k(this)f
(problem)f(of)i(small)f(t)m(wist)i(can)e(b)s(e)g(solv)m(ed)h(with)f
(the)g(help)g(of)165 3156 y(the)e(higher)g(order)f(term)h(in)g(the)g
(righ)m(t)h(hand)d(side)i(of)56 b(_)-50 b Fp(')q Fv(,)31
b(using)g(a)g(mild)g(non-degeneracy)g(condition)165 3269
y(on)f Fp(\020)331 3283 y Fo(2)401 3269 y Fv(\(and)g(th)m(us)g(on)g
Fp(Z)7 b Fv(\).)165 3721 y Fd(3.4)112 b(Dynamical)39
b(instabilit)m(y)165 3892 y Fv(Still)29 b(assuming)g(a)m(v)r(\()p
Fp(a)p Fv(\))d Fp(>)f Fv(0)k(w)m(e)h(no)m(w)e(consider)h(the)g(case)h
(a)m(v)r(\()p Fp(b)p Fv(\))c Fp(<)f Fv(0.)41 b(T)-8 b(o)29
b(a)m(v)m(oid)i(negativ)m(e)g(constan)m(ts)165 4005 y(w)m(e)g(de\014ne)
e Fp($)f Fv(:=)e Fq(\000)15 b Fv(a)m(v)r(\()p Fp(b)p
Fv(\))26 b Fp(>)f Fv(0)30 b(whence)1027 4209 y Fp(a)p
Fv(\()p Fp(t)p Fv(\))c(=)f(a)m(v)r(\()p Fp(a)p Fv(\))c(+)f
Fp(a)1670 4223 y Fo(1)1709 4209 y Fv(\()p Fp(t)p Fv(\))92
b(and)e Fp(b)p Fv(\()p Fp(t)p Fv(\))26 b(=)f Fq(\000)p
Fp($)d Fv(+)e Fp(b)2703 4223 y Fo(1)2743 4209 y Fv(\()p
Fp(t)p Fv(\))165 4413 y(with)30 b(a)m(v)r(\()p Fp(a)547
4427 y Fo(1)587 4413 y Fv(\))c(=)f(a)m(v)r(\()p Fp(b)910
4427 y Fo(1)949 4413 y Fv(\))h(=)f(0.)41 b(Replacing)32
b(\(3)p Fp(:)p Fv(3\))g(b)m(y)e(an)g(`auxiliary')i(system)1483
4534 y Fg(8)1483 4609 y(>)1483 4634 y(<)1483 4783 y(>)1483
4808 y(:)1615 4618 y Fv(_)-41 b Fp(x)83 b Fv(=)f(a)m(v)s(\()p
Fp(a)p Fv(\))p Fp(y)2146 4585 y Fo(2)p Fn(m)p Fo(+1)1615
4844 y Fv(_)-41 b Fp(y)90 b Fv(=)121 b Fq(\000)p Fp($)s(x)2127
4811 y Fo(2)p Fn(n)p Fo(+1)3476 4731 y Fv(\(3.10\))165
5050 y(w)m(e)41 b(obtain)h(again)g(a)f(p)s(erio)s(dic)f(\015o)m(w)h
(de\014ning)f(the)h(transformation)g(\010)g(in)g(\(3)p
Fp(:)p Fv(5\).)74 b(The)40 b(Hamilto-)165 5163 y(nian)30
b(\(3)p Fp(:)p Fv(2\))i(no)m(w)e(turns)g(in)m(to)1236
5425 y(\010)1302 5388 y Fx(\003)1341 5425 y Fp(H)7 b
Fv(\()p Fp(\032;)15 b(';)g(t)p Fv(\))27 b(=)1846 5364
y Fp(\032)1893 5331 y Fn(\016)p 1846 5404 85 4 v 1866
5488 a Fp(\016)1941 5425 y(d)p Fv(\()p Fp(')p Fv(\))21
b(+)f Fp(h)2281 5439 y Fo(1)2321 5425 y Fv(\()p Fp(\032;)15
b(';)g(t)p Fv(\))p Fp(:)1891 5691 y Fv(21)p eop end
%%Page: 22 22
TeXDict begin 22 21 bop 165 337 a Fv(with)30 b Fp(h)424
351 y Fo(1)494 337 y Fv(still)h(giv)m(en)h(b)m(y)e(\(3)p
Fp(:)p Fv(7\))i(and)921 517 y Fp(d)p Fv(\()p Fp(')p Fv(\))85
b(=)d Fp(\014)5 b(c)1430 479 y Fn(\016)1474 517 y Fv(a)m(v)r(\()p
Fp(a)p Fv(\))p Fp(C)1756 479 y Fo(2)p Fn(m)p Fo(+2)1948
517 y Fv(\()p Fp('T)2095 531 y Fo(0)2136 517 y Fv(\))20
b Fq(\000)g Fp(\013c)2379 479 y Fn(\016)2418 517 y Fp($)s(S)2557
479 y Fo(2)p Fn(n)p Fo(+2)2729 517 y Fv(\()p Fp('T)2876
531 y Fo(0)2916 517 y Fv(\))165 697 y(where)42 b(in)g
Fq(x)g Fv(3.2)i(the)e(expression)g Fp(d)p Fv(\()p Fp(')p
Fv(\))47 b Fq(\021)e Fp(\014)5 b(c)1851 664 y Fn(\016)1889
697 y Fv(a)m(v)r(\()p Fp(a)p Fv(\))43 b(w)m(as)g Fp(')p
Fv(-indep)s(enden)m(t.)76 b(The)42 b(real)h(analytic)165
810 y(function)30 b Fp(d)h Fv(is)f(1-p)s(erio)s(dic)g(in)h
Fp(')p Fv(,)g(and)e(from)1012 990 y Fp(\014)5 b(c)1107
952 y Fn(\016)1151 990 y Fv(a)m(v)r(\()p Fp(a)p Fv(\))p
Fp(C)1433 952 y Fo(2)p Fn(m)p Fo(+2)1625 990 y Fv(\()p
Fp(t)p Fv(\))21 b(+)f Fp(\013c)1937 952 y Fn(\016)1975
990 y Fp($)s(S)2114 952 y Fo(2)p Fn(n)p Fo(+2)2287 990
y Fv(\()p Fp(t)p Fv(\))25 b Fq(\021)g Fp(\014)5 b(c)2606
952 y Fn(\016)2650 990 y Fv(a)m(v)r(\()p Fp(a)p Fv(\))616
b(\(3.11\))165 1170 y(w)m(e)31 b(deduce)1151 1308 y Fp(d)p
Fv(\()p Fp(')p Fv(\))c(=)e(2)p Fp(\013c)1592 1270 y Fn(\016)1631
1308 y Fp($)1724 1189 y Fg(\024)1778 1246 y Fp(\014)20
b Fv(a)m(v)r(\()p Fp(a)p Fv(\))p 1778 1287 283 4 v 1828
1370 a(2)p Fp(\013$)2090 1308 y Fq(\000)g Fp(S)2242 1270
y Fo(2)p Fn(n)p Fo(+2)2415 1308 y Fv(\()p Fp('T)2562
1322 y Fo(0)2602 1308 y Fv(\))2637 1189 y Fg(\025)2696
1308 y Fp(:)165 1499 y Fv(The)j(original)h(v)m(ector)h(\014eld)d
Fp(X)1181 1524 y Fc(H)1267 1499 y Fv(+)6 b Fp(Y)26 b
Fv(+)6 b Fp(Z)29 b Fv(is)23 b(transformed)g(in)m(to)h
Fp(X)2414 1524 y Ft(\010)2474 1494 y Fb(\003)2512 1524
y Fc(H)2598 1499 y Fv(+)6 b(\010)2741 1466 y Fx(\003)2779
1499 y Fp(Y)26 b Fv(+)6 b(\010)3001 1466 y Fx(\003)3040
1499 y Fp(Z)30 b Fv(with)22 b(equations)165 1612 y(of)30
b(motion)1147 1719 y(_)-44 b Fp(\032)83 b Fv(=)1422 1678
y Fn(\032)1458 1654 y Ff(\016)p 1422 1697 71 4 v 1440
1750 a Fn(\016)1502 1719 y Fp(d)1549 1686 y Fx(0)1573
1719 y Fv(\()p Fp(')p Fv(\))21 b(+)f Fp(\021)1859 1733
y Fo(1)1899 1719 y Fv(\()p Fp(\032;)15 b(';)g(t)p Fv(\))22
b(+)d Fp(\020)2340 1733 y Fo(1)2380 1719 y Fv(\()p Fp(\032;)c(';)g(t)p
Fv(\))1140 1856 y(_)-49 b Fp(')83 b Fv(=)g Fp(\032)1459
1823 y Fn(\016)r Fx(\000)p Fo(1)1587 1856 y Fp(d)p Fv(\()p
Fp(')p Fv(\))22 b(+)e Fp(\021)1921 1870 y Fo(2)1960 1856
y Fv(\()p Fp(\032;)15 b(';)g(t)p Fv(\))22 b(+)e Fp(\020)2402
1870 y Fo(2)2441 1856 y Fv(\()p Fp(\032;)15 b(';)g(t)p
Fv(\))p Fp(:)3476 1778 y Fv(\(3.12\))165 2004 y(The)30
b(expressions)g(at)h(the)f(righ)m(t)h(hand)f(side)g(are)h(again)g
(de\014ned)e(b)m(y)1320 2221 y Fp(X)1380 2248 y Fc(h)1428
2260 y Fa(1)1489 2221 y Fv(+)20 b(\010)1646 2184 y Fx(\003)1685
2221 y Fp(Y)103 b Fv(=:)83 b Fp(\021)2065 2235 y Fo(1)2138
2160 y Fp(@)p 2115 2200 101 4 v 2115 2284 a(@)5 b(\032)2245
2221 y Fv(+)20 b Fp(\021)2381 2235 y Fo(2)2460 2160 y
Fp(@)p 2431 2200 113 4 v 2431 2284 a(@)5 b(')1585 2459
y Fv(\010)1651 2422 y Fx(\003)1690 2459 y Fp(Z)89 b Fv(=:)83
b Fp(\020)2060 2473 y Fo(1)2133 2398 y Fp(@)p 2109 2438
101 4 v 2109 2522 a(@)5 b(\032)2240 2459 y Fv(+)20 b
Fp(\020)2371 2473 y Fo(2)2450 2398 y Fp(@)p 2420 2438
113 4 v 2420 2522 a(@)5 b(')165 2678 y Fv(and)30 b(still)h(satisfy)628
2858 y Fp(\021)673 2872 y Fo(1)738 2858 y Fv(=)25 b Fp(o)p
Fv(\()p Fp(\032)960 2820 y Fn(\034)1004 2858 y Fv(\))p
Fp(;)107 b(\021)1216 2872 y Fo(2)1280 2858 y Fv(=)25
b Fp(o)p Fv(\()p Fp(\032)1502 2820 y Fn(\033)1550 2858
y Fv(\))p Fp(;)106 b(\020)1756 2872 y Fo(1)1821 2858
y Fv(=)25 b Fp(o)p Fv(\()p Fp(\032)2043 2820 y Fn(\016)2081
2858 y Fv(\))p Fp(;)107 b(\020)2288 2872 y Fo(2)2352
2858 y Fv(=)25 b Fp(o)p Fv(\()p Fp(\032)2574 2820 y Fo(2)p
Fn(\033)2657 2858 y Fv(\))182 b(as)30 b Fp(\032)c Fq(!)f
Fv(0.)165 3038 y(As)30 b(in)g Fq(x)h Fv(3.3)g(w)m(e)g(use)f(the)h
(time-)p Fp(t)p Fv(-mapping)g(\011)1785 3052 y Fn(t)1844
3038 y Fv(of)g(the)g(`auxiliary')g(v)m(ector)h(\014eld)1088
3256 y Fp(W)13 b Fv(\()p Fp(\032;)i(';)g(t)p Fv(\))27
b(=)e Fq(\000)p Fp(\021)1715 3270 y Fo(1)1754 3256 y
Fv(\()p Fp(\032;)15 b(';)g(t)p Fv(\))2079 3194 y Fp(@)p
2053 3235 101 4 v 2053 3318 a(@)5 b(\032)2186 3256 y
Fq(\000)19 b Fp(\021)2321 3270 y Fo(2)2361 3256 y Fv(\()p
Fp(\032;)c(';)g(t)p Fv(\))2692 3194 y Fp(@)p 2660 3235
113 4 v 2660 3318 a(@)5 b(')165 3479 y Fv(to)31 b(transform)f(\(3)p
Fp(:)p Fv(12\))i(in)m(to)1443 3609 y(_)-44 b Fp(\045)83
b Fv(=)g Fq(\000)1789 3568 y Fn(\045)1825 3545 y Ff(\016)p
1789 3588 71 4 v 1807 3640 a Fn(\016)1869 3609 y Fp(d)1916
3576 y Fx(0)1939 3609 y Fv(\()p Fp(#)p Fv(\))21 b(+)f
Fp(o)p Fv(\()p Fp(\045)2301 3576 y Fn(\016)2339 3609
y Fv(\))1439 3728 y(_)1417 3752 y Fp(#)83 b Fv(=)g Fp(\045)1755
3719 y Fn(\016)r Fx(\000)p Fo(1)1883 3752 y Fp(d)p Fv(\()p
Fp(#)p Fv(\))21 b(+)f Fp(o)p Fv(\()p Fp(\045)2292 3719
y Fn(\016)r Fx(\000)p Fo(1)2420 3752 y Fv(\))3476 3671
y(\(3.13\))165 3905 y(preserving)30 b(the)g(conserv)-5
b(ativ)m(e)33 b(nature)d(\(rev)m(ersible)h(and/or)g(Hamiltonian\))h(of)
e(the)h(system.)306 4018 y(The)i(phase)g(p)s(ortrait)h(of)f(\(3)p
Fp(:)p Fv(10\))j(is)d(rev)m(ersible)i(with)e(resp)s(ect)g(to)h(the)g
(re\015ections)g(ab)s(out)f(the)h Fp(x)p Fv(-)165 4130
y(axis)29 b(and)g(ab)s(out)f(the)h Fp(y)s Fv(-axis,)h(whence)f(b)s(oth)
f Fp(S)34 b Fv(and)28 b Fp(C)36 b Fv(are)29 b(p)s(ositiv)m(e)h(on)f
(\(0)p Fp(;)2861 4095 y Fo(1)p 2861 4110 36 4 v 2861
4162 a(4)2906 4130 y Fp(T)2959 4144 y Fo(0)2999 4130
y Fv(\))g(with)f Fp(S)5 b Fv(\(0\))27 b(=)e(0)g(=)165
4243 y Fp(C)7 b Fv(\()282 4208 y Fo(1)p 282 4223 V 282
4275 a(4)327 4243 y Fp(T)380 4257 y Fo(0)419 4243 y Fv(\))31
b(at)g(the)g(b)s(oundary)-8 b(.)39 b(In)30 b(particular)1191
4470 y Fp(d)p Fv(\(0\))d(=)e Fp(\014)5 b(c)1571 4433
y Fn(\016)1615 4470 y Fv(a)m(v)r(\()p Fp(a)p Fv(\))p
Fp(;)107 b(d)p Fv(\()2049 4409 y(1)p 2049 4449 46 4 v
2049 4533 a(4)2105 4470 y(\))26 b(=)e Fq(\000)p Fp(\014)5
b(c)2427 4433 y Fn(\016)2471 4470 y Fv(a)m(v)r(\()p Fp(a)p
Fv(\))165 4676 y(b)s(ecause)30 b(of)h(\(3)p Fp(:)p Fv(11\))h(and)978
4856 y Fp(d)1025 4819 y Fx(0)1049 4856 y Fv(\()p Fp(#)p
Fv(\))26 b(=)f Fq(\000)p Fv(2)p Fp(\016)s(c)1493 4819
y Fn(\016)1537 4856 y Fv(a)m(v)r(\()p Fp(a)p Fv(\))p
Fp($)19 b(T)1894 4870 y Fo(0)1949 4856 y Fp(S)2010 4819
y Fo(2)p Fn(n)p Fo(+1)2182 4856 y Fv(\()p Fp(#T)2324
4870 y Fo(0)2364 4856 y Fv(\))c Fp(C)2486 4819 y Fo(2)p
Fn(m)p Fo(+1)2678 4856 y Fv(\()p Fp(#T)2820 4870 y Fo(0)2859
4856 y Fv(\))165 5036 y(is)36 b(negativ)m(e)h(for)f(all)g
Fp(#)e Fq(2)g Fv(\(0)p Fp(;)1215 5001 y Fo(1)p 1215 5016
36 4 v 1215 5068 a(4)1260 5036 y Fv(\).)57 b(Therefore)35
b Fp(d)h Fv(has)g(a)g(unique)e(ro)s(ot)i Fp(#)2680 5003
y Fx(\003)2754 5036 y Fq(2)d Fv(\(0)p Fp(;)2979 5001
y Fo(1)p 2979 5016 V 2979 5068 a(4)3025 5036 y Fv(\))j(and)f(there)h
(is)f(an)165 5149 y(op)s(en)28 b(in)m(terv)-5 b(al)29
b(\()p Fp(#)798 5116 y Fx(\003)854 5149 y Fq(\000)16
b Fp(&)7 b(;)15 b(#)1075 5116 y Fx(\003)1131 5149 y Fv(+)h
Fp(&)7 b Fv(\))26 b Fq(\022)f Fv(\(0)p Fp(;)1546 5113
y Fo(1)p 1546 5128 V 1546 5181 a(4)1591 5149 y Fv(\))k(on)f(whic)m(h)g
Fp(d)h Fv(is)f(monotonously)h(decreasing)g(with)f(p)s(ostiv)m(e)165
5262 y(v)-5 b(alues)31 b(on)f(\()p Fp(#)651 5229 y Fx(\003)711
5262 y Fq(\000)19 b Fp(&)7 b(;)15 b(#)935 5229 y Fx(\003)975
5262 y Fv(\))31 b(and)f(negativ)m(e)i(v)-5 b(alues)31
b(on)f(\()p Fp(#)2062 5229 y Fx(\003)2102 5262 y Fp(;)15
b(#)2196 5229 y Fx(\003)2256 5262 y Fv(+)20 b Fp(&)7
b Fv(\).)41 b(On)29 b(the)i(region)994 5442 y(\003)25
b(=)g Fq(f)p Fv(\()p Fp(\045;)15 b(#;)g(t)p Fv(\))27
b Fq(2)e Fh(R)1680 5405 y Fo(3)1744 5442 y Fv(:)h Fp(\045)f(>)g
Fv(0)p Fp(;)15 b(#)2102 5405 y Fx(\003)2162 5442 y Fq(\000)20
b Fp(&)33 b(<)25 b(#)g(<)f(#)2643 5405 y Fx(\003)2703
5442 y Fv(+)c Fp(&)7 b Fq(g)1891 5691 y Fv(22)p eop end
%%Page: 23 23
TeXDict begin 23 22 bop 165 337 a Fv(w)m(e)31 b(consider)f(the)h
(function)1126 541 y Fp(V)46 b Fv(=)25 b Fp(\045)1368
503 y Fn(\016)1421 541 y Fv(sin)15 b Fp(\036)91 b Fv(with)f
Fp(\036)26 b Fv(=)2161 479 y Fp(\031)p 2146 520 86 4
v 2146 603 a Fv(2)p Fp(&)2241 541 y Fv(\()p Fp(#)21 b
Fq(\000)f Fp(#)2496 503 y Fx(\003)2555 541 y Fv(+)g Fp(&)7
b Fv(\))p Fp(:)165 775 y Fv(Then)29 b Fp(V)46 b(>)25
b Fv(0)30 b(in)g(\003)h(and)f Fp(V)45 b Fv(=)25 b(0)31
b(on)f Fp(@)5 b Fv(\003,)31 b(the)g(b)s(oundary)d(of)j(\003.)40
b(It)31 b(follo)m(ws)g(that)741 955 y Fp(dV)p 741 996
121 4 v 761 1079 a(dt)872 894 y Fg(\014)872 944 y(\014)872
994 y(\014)872 1044 y(\014)899 1098 y Fo(\(3)p Fn(:)p
Fo(13\))1167 1017 y Fv(=)1331 955 y Fp(@)5 b(V)p 1331
996 127 4 v 1344 1079 a(@)g(\045)1486 1017 y Fv(_)-44
b Fp(\045)20 b Fv(+)1635 955 y Fp(@)5 b(V)p 1635 996
V 1645 1079 a(@)g(#)1793 993 y Fv(_)1772 1017 y Fp(#)20
b Fv(+)1947 955 y Fp(@)5 b(V)p 1947 996 V 1967 1079 a(@)g(t)1167
1270 y Fv(=)83 b Fp(\045)1368 1232 y Fo(2)p Fn(\016)r
Fx(\000)p Fo(1)1546 1151 y Fg(\024)1590 1270 y Fq(\000)p
Fp(d)1708 1232 y Fx(0)1731 1270 y Fv(\()p Fp(#)p Fv(\))15
b(sin)h Fp(\036)k Fv(+)2188 1208 y Fp(\031)p 2173 1249
86 4 v 2173 1332 a Fv(2)p Fp(&)2269 1270 y(d)p Fv(\()p
Fp(#)p Fv(\))15 b(cos)h Fp(\036)2646 1151 y Fg(\025)2711
1270 y Fv(+)j Fp(o)p Fv(\()p Fp(\045)2927 1232 y Fo(2)p
Fn(\016)r Fx(\000)p Fo(1)3091 1270 y Fv(\))p Fp(:)165
1515 y Fv(F)-8 b(or)45 b Fp(#)k Fq(2)f Fv(\()p Fp(#)643
1482 y Fx(\003)682 1515 y Fp(;)15 b(#)776 1482 y Fx(\003)846
1515 y Fv(+)29 b Fp(&)7 b Fv(\),)49 b(w)m(e)44 b(ha)m(v)m(e)1476
1479 y Fn(\031)p 1476 1494 43 4 v 1480 1546 a Fo(2)1578
1515 y Fp(<)1719 1479 y Fn(\031)p 1707 1494 67 4 v 1707
1546 a Fo(2)p Fn(&)1783 1515 y Fv(\()p Fp(#)30 b Fq(\000)f
Fp(#)2056 1482 y Fx(\003)2125 1515 y Fv(+)g Fp(&)7 b
Fv(\))50 b(=)e Fp(\036)h(<)f(\031)g Fv(so)c(that)i(cos)15
b Fp(\036)49 b(<)g Fv(0.)83 b(It)165 1628 y(follo)m(ws)36
b(that)g Fq(\000)p Fp(d)788 1595 y Fx(0)811 1628 y Fv(\()p
Fp(#)p Fv(\))15 b(sin)h Fp(\036)23 b Fv(+)1271 1592 y
Fn(\031)p 1259 1607 V 1259 1659 a Fo(2)p Fn(&)1336 1628
y Fp(d)p Fv(\()p Fp(#)p Fv(\))15 b(cos)i Fp(\036)33 b(>)g
Fv(0)j(for)f Fp(#)e Fq(2)g Fv(\()p Fp(#)2346 1595 y Fx(\003)2386
1628 y Fp(;)15 b(#)2480 1595 y Fx(\003)2543 1628 y Fv(+)23
b Fp(&)7 b Fv(\).)56 b(Similarly)-8 b(,)37 b(w)m(e)f(also)g(ha)m(v)m(e)
165 1741 y Fq(\000)p Fp(d)283 1708 y Fx(0)306 1741 y
Fv(\()p Fp(#)p Fv(\))15 b(sin)h Fp(\036)22 b Fv(+)764
1705 y Fn(\031)p 753 1720 V 753 1772 a Fo(2)p Fn(&)829
1741 y Fp(d)p Fv(\()p Fp(#)p Fv(\))15 b(cos)i Fp(\036)31
b(>)g Fv(0)j(for)g Fp(#)d Fq(2)f Fv(\()p Fp(#)1827 1708
y Fx(\003)1890 1741 y Fq(\000)22 b Fp(&)7 b(;)15 b(#)2117
1708 y Fx(\003)2157 1741 y Fv(\).)51 b(Since)34 b Fq(\000)p
Fp(d)2627 1708 y Fx(0)2651 1741 y Fv(\()p Fp(#)2740 1708
y Fx(\003)2779 1741 y Fv(\))e Fp(>)f Fv(0)j(w)m(e)g(conclude)g(that)185
1848 y Fn(dV)p 185 1863 94 4 v 200 1915 a(dt)288 1787
y Fg(\014)288 1836 y(\014)288 1886 y(\014)316 1940 y
Fo(\(3)p Fn(:)p Fo(13\))525 1884 y Fp(>)25 b Fv(0)j(on)f(\003,)h(if)f
Fp(\045)g Fv(is)g(su\016cien)m(tly)h(small.)40 b(It)27
b(follo)m(ws)h(from)f(Chetaev's)h(theorem)f([6)q(])g(that)h(the)165
2033 y(trivial)j(solution)g(of)g(\(3.1\))h(is)e(unstable.)2098
b Fq(u)-61 b(t)165 2246 y Fj(Remark)35 b(3.9)46 b Fv(F)-8
b(or)32 b Fp(m)26 b Fv(=)g Fp(n)g Fv(=)g(0)32 b(the)f(h)m(yp)s(erb)s
(olic)f(linear)i(system)f(\(3)p Fp(:)p Fv(3\))i(implies)e(dynamical)g
(insta-)165 2359 y(bilit)m(y)g(of)g(\()p Fp(x;)15 b(y)s
Fv(\))26 b(=)f(\(0)p Fp(;)15 b Fv(0\))32 b(for)e Fp(X)1269
2384 y Fc(H)1370 2359 y Fv(+)20 b Fp(Z)36 b Fv(as)31
b(w)m(ell.)306 2807 y Fj(A)m(CKNO)m(WLEDGMENT)306 2920
y Fv(The)45 b(authors)g(are)h(v)m(ery)g(grateful)g(to)g(an)g(anon)m
(ymous)f(referee)h(for)g(helpful)e(commen)m(ts)j(and)165
3033 y(suggestions.)165 3320 y Fr(References)215 3523
y Fv([1])g(V.I.)35 b(Arnol'd,)i(S.M.)e(Gusein-Zade)h(and)e(A.N.)i(V)-8
b(arc)m(henk)m(o,)39 b Fi(Singularities)f(of)f(Di\013er)-5
b(entiable)357 3636 y(Maps,)33 b(V)-7 b(ol.)32 b(1)p
Fv(,)g(Birkh\177)-45 b(auser)29 b(\(1985\))215 3823 y([2])47
b(Y)-8 b(u.N.)37 b(Bibik)m(o)m(v,)k(Stabilit)m(y)d(of)f(Zero)g
(Solutions)g(of)g(Essen)m(tially)h(Nonlinear)f(One-Degree-Of-)357
3936 y(F)-8 b(reedom)27 b(Hamiltonian)h(and)e(Rev)m(ersible)h(Systems,)
g Fi(Di\013er)-5 b(ential)30 b(Equations)d Fj(38)f Fv(\(2002\))j(609{)
357 4049 y(614)215 4237 y([3])47 b(A.)32 b(Berretti)h(and)f(G.)g(Gen)m
(tile,)j(Bryuno)c(F)-8 b(unction)33 b(and)e(the)h(Standard)f(Map,)i
Fi(Comm.)i(Math.)357 4350 y(Phys.)30 b Fj(220)i Fv(\(2001\))g(623{656)
215 4537 y([4])47 b(H.W.)35 b(Bro)s(er,)h(G.B.)f(Huitema)h(and)d(M.B.)j
(Sevryuk,)e Fi(Quasi-Perio)-5 b(dic)37 b(Motions)g(in)f(F)-7
b(amilies)357 4650 y(of)33 b(Dynamic)-5 b(al)34 b(Systems:)42
b(Or)-5 b(der)34 b(amidst)g(Chaos)p Fv(,)e(LNM)f Fj(1645)p
Fv(,)g(Springer)e(\(1996\))215 4838 y([5])47 b(T.)28
b(Carletti)h(and)f(S.)g(Marmi,)h(Linearization)h(of)e(analytic)i(and)e
(non-analytic)i(germs)e(of)g(di\013eo-)357 4951 y(morphisms)h(of)h(\()p
Fh(C)p Fp(;)15 b Fv(0\),)32 b Fi(Bul)5 b(l.)33 b(So)-5
b(c.)33 b(Math.)g(F)-7 b(r)i(anc)g(e)32 b Fj(128)f Fv(\(2000\))i(69{85)
215 5138 y([6])47 b(N.)31 b(Chetaev,)g Fi(The)i(stability)g(of)g
(motion)p Fv(,)f(Oxford:)40 b(P)m(ergamon)31 b(\(1961\))215
5326 y([7])47 b(B.)24 b(Liu,)h(The)e(stabilit)m(y)i(of)f(the)f
(equilibrium)g(of)h(a)g(conserv)-5 b(ativ)m(e)25 b(system,)h
Fi(J.)g(Math.)g(A)n(nal.)h(Appl.)357 5439 y Fj(202)k
Fv(\(1996\))i(133{149)1891 5691 y(23)p eop end
%%Page: 24 24
TeXDict begin 24 23 bop 215 337 a Fv([8])47 b(B.)38 b(Liu,)h(The)e
(stabilit)m(y)i(of)f(the)g(equilibrium)f(of)g(rev)m(ersible)i(systems,)
g Fi(T)-7 b(r)i(ans.)41 b(A)n(mer.)e(Math.)357 450 y(So)-5
b(c.)31 b Fj(351)g Fv(\(1999\))i(515{531)215 637 y([9])47
b(B.)34 b(Liu,)g(The)f(Stabilit)m(y)i(of)f(the)g(Equilibrium)e(of)i
(Planar)g(Hamiltonian)h(and)e(Rev)m(ersible)h(sys-)357
750 y(tems,)d Fi(J.)h(Dynamics)h(Di\013.)f(Eq.)d Fj(18)i
Fv(\(2006\))i(975{990)170 938 y([10])47 b(J.)29 b(Moser,)i(Con)m(v)m
(ergen)m(t)h(Series)d(Expansion)g(for)h(Quasi-P)m(erio)s(dic)h
(Motions,)g Fi(Math.)h(A)n(nn.)d Fj(169)357 1051 y Fv(\(1967\))k
(136{176)170 1238 y([11])47 b(J.)24 b(Moser,)i Fi(Stable)i(and)f(R)-5
b(andom)30 b(Motions)d(in)g(Dynamic)-5 b(al)28 b(Systems:)40
b(With)27 b(Sp)-5 b(e)g(cial)29 b(Emphasis)357 1351 y(on)k(Celestial)g
(Me)-5 b(chanics)p Fv(,)31 b(Princeton)g(Univ.)f(Press)g(\(1973\))170
1539 y([12])47 b(D.)39 b(N)s(\023)-48 b(u)s(~)g(nez)39
b(and)f(R.)h(Ortega,)j(P)m(arab)s(olic)e(\014xed)e(p)s(oin)m(t)h(and)f
(stabilit)m(y)j(criteria)f(for)e(nonlinear)357 1652 y(Hill's)31
b(equation,)h Fi(Z.)g(angew.)h(Math.)g(Phys.)d Fj(51)h
Fv(\(2000\))i(890{911)170 1839 y([13])47 b(R.)35 b(Ortega,)i(The)e
(stabilit)m(y)i(of)e(the)g(equilibrium)f(of)i(a)f(nonlinear)g(Hill's)h
(equation,)h Fi(SIAM)g(J.)357 1952 y(Math.)c(A)n(nal.)d
Fj(25)h Fv(\(1994\))i(1394{1401)170 2140 y([14])47 b(R.)28
b(P)m(\023)-43 b(erez-Marco)31 b(and)c(J.-C.)h(Y)-8 b(o)s(ccoz,)31
b(Germes)d(de)g(feulletages)i(holomorphes)d(\022)-45
b(a)28 b(holomie)h(pre-)357 2253 y(scrite,)i Fi(Ast)n(\023)-44
b(erisque)30 b Fj(222)h Fv(\(1994\))i(345{371)170 2440
y([15])47 b(J.)40 b(P\177)-45 b(osc)m(hel,)45 b(A)40
b(lecture)h(on)g(the)g(classical)h(KAM)f(theorem,)i Fi(Pr)-5
b(o)g(c.)43 b(Symp.)g(Pur)-5 b(e)42 b(Math.)f Fj(69)357
2553 y Fv(\(2001\))33 b(707{732)170 2741 y([16])47 b(H.)40
b(R)s(\177)-48 b(ussmann,)42 b(In)m(v)-5 b(arian)m(t)41
b(tori)g(in)f(non-degenerate)h(nearly)g(in)m(tegrable)h(Hamiltonian)f
(sys-)357 2854 y(tems,)31 b Fi(R)-5 b(e)g(g.)33 b(&)f(Chaot.)i(Dyn.)c
Fj(6)h Fv(\(2001\))i(119{204)170 3041 y([17])47 b(H.)34
b(R)s(\177)-48 b(ussmann,)33 b(Stabilit)m(y)i(of)f(elliptic)h(\014xed)e
(p)s(oin)m(ts)g(of)h(analytic)h(area-preserving)g(mappings)357
3154 y(under)29 b(the)h(Bruno)g(condition,)h Fi(Er)-5
b(go)g(d.)34 b(Th.)f(&)f(Dynam.)h(Sys.)e Fj(22)g Fv(\(2002\))i
(1551{1573)170 3342 y([18])47 b(C.L.)30 b(Siegel)i(and)d(J.K.)i(Moser,)
g Fi(L)-5 b(e)g(ctur)g(es)33 b(on)g(Celestial)h(Me)-5
b(chanics)p Fv(,)31 b(Springer)e(\(1971\))170 3530 y([19])47
b(J.-C.)36 b(Y)-8 b(o)s(ccoz,)40 b(Lin)m(\023)-43 b(earization)39
b(des)d(germes)g(de)g(di\013)m(\023)-43 b(eomorphismes)37
b(holomorphes)e(de)h(\()p Fh(C)p Fp(;)15 b Fv(0\),)357
3643 y Fi(C.)32 b(R.)h(A)-5 b(c)g(ad.)33 b(Sci.)g(Paris)d
Fj(306)i Fv(\(1988\))g(55{58)170 3830 y([20])47 b(J.-C.)30
b(Y)-8 b(o)s(ccoz,)33 b(P)m(etit)f(diviseurs)e(en)g(dimension)g(1,)h
Fi(Ast)n(\023)-44 b(erisque)30 b Fj(231)h Fv(\(1995\))1891
5691 y(24)p eop end
%%Trailer

userdict /end-hook known{end-hook}if
%%EOF