This is a multi-part message in MIME format. ---------------0003310731378 Content-Type: text/plain; name="00-134.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="00-134.keywords" Nekhoroshev theorem ---------------0003310731378 Content-Type: application/postscript; name="bande3.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="bande3.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: bande3.dvi %%Pages: 30 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips bande3 %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2000.03.31:0932 %%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: special.pro %! 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1 111 C 1 -24 C 1 -10 C 2 17 C 1 84 C 1 -14 C 1 287 C 2 62 C 1 -180 C 1 -234 C 1 2 C 2 105 C 1 169 C 1 23 C 1 -197 C 2 -35 C 1 128 C 1 -233 C 1 1 C 2 304 C 1 11 C 1 -214 C 1 -35 C 2 204 C 1 -135 C 1 -375 C 2 596 C 1 98 C 1 -136 C 1 -17 C 2 -172 C 1 -42 C 1 39 C 1 243 C 2 73 C 1 -252 C 1 -27 C 1 108 C 2 23 C 1 -168 C 1 163 C 1 23 C 2 -392 C 1 283 C 1 282 C 1 1 C 2 -93 C 1 283 C 1 -38 C 1 -181 C 2 155 C 1 -20 C 1 -208 C 2 -17 C 1 190 C 1 -30 C 1 -97 C 2 88 C 1 -38 C 1 -177 C 1 13 C 2 -176 C 1 342 C 1 113 C 1 -158 C 2 -70 C 1 67 C 1 -31 C 1 -64 C 2 -9 C 1 37 C 1 78 C 1 30 C 2 48 C 1 -89 C 1 -15 C 1 28 C 2 128 C 1 -21 C 1 -155 C 1 378 C 2 3 C 1 -327 C 1 -402 C 2 360 C 1 138 C 1 154 C 1 33 C 2 -102 C 1 23 C 1 49 C 1 -159 C 2 82 C 1 125 C 1 -34 C 1 -231 C 2 66 C 1 86 C 1 -113 C 1 -115 C 2 42 C 1 40 C 1 -31 C 1 -24 C 2 142 C 1 -67 C 1 -48 C 1 -132 C 2 149 C 1 52 C 1 168 C 1 5 C 2 -285 C 1 -78 C 1 167 C 2 45 C 1 -140 C 1 22 C 1 -44 C 2 -2 C 1 136 C 1 -30 C 1 -123 C 2 88 C 1 208 C 1 -92 C 1 -225 C 2 211 C 1 43 C 1 -14 C 1 -169 C 2 180 C 1 83 C 1 153 C 1 -3 C 2 -227 C 1 55 C 1 -66 C 1 -29 C 2 -106 C 1 -39 C 1 59 C 1 8 C 2 63 C 1 111 C 1 -160 C 2 -13 C 1 173 C 1 1 C 1 59 C 2 -32 C 1 -57 C 1 -11 C 1 101 C 2 41 C 1 -42 C 1 -26 C 1 -39 C 2 -105 C 1 29 C 1 55 C 1 -50 C 2 -78 C 1 233 C 1 -23 C 1 -180 C 2 -17 C 1 9 C 1 -13 C 1 155 C 2 -45 C 1 73 C 1 -31 C 1 -74 C 2 -144 C 1 103 C 1 109 C 2 -66 C 1 -319 C 1 391 C 1 7 C 2 -137 C 1 -98 C 1 259 C 1 4 C 2 18 C 1 20 C 1 -24 C 1 -26 C 2 -14 C 1 -87 C 1 -39 C 1 -103 C 2 -7 C 1 153 C 1 132 C 1 -36 C 2 147 C 1 37 C 1 -24 C 1 -169 C 2 125 C 1 16 C 1 -60 C 1 9 C 2 -131 C 1 22 C 1 120 C 2 -186 C 1 236 C 1 73 C 1 -105 C 2 -77 C 1 167 C 1 -67 C 1 66 C 2 4 C 1 -16 C 1 -119 C 1 29 C 2 117 C 1 -252 C 1 211 C 1 121 C 2 -179 C 1 -173 C 1 3 C 1 113 C 2 -54 C 1 29 C 1 -13 C 1 56 C 2 98 C 1 -97 C 1 -58 C 1 141 C 2 104 C 1 -84 C 1 -152 C 2 148 C 1 151 C 1 -32 C 1 6 C 2 -64 C 1 42 C 1 -27 C 1 -134 C 2 -75 C 1 124 C 1 -129 C 1 -117 C 2 175 C 1 41 C 1 108 C 1 -196 C 2 83 C 1 -238 C 1 163 C 1 106 C 2 -57 C 1 43 C 1 8 C 1 -30 C 2 -138 C 1 12 C 1 -27 C 2 95 C 1 67 C 1 3 C 1 -50 C 2 -42 C 1 -155 C 1 358 C 1 -18 C 2 132 C 1 -38 C 1 -106 C 1 -163 C 2 -121 C 1 -61 C 1 203 C 1 30 C 2 64 C 1 141 C 1 -194 C 1 3 C 2 -306 C 1 65 C 1 77 C 1 198 C 2 74 C 1 -133 C 1 -142 C 1 12 C 2 139 C 1 275 C 1 -6 C 2 -269 C 1 -86 C 1 181 C 1 -7 C 2 -271 C 1 159 C 1 108 C 1 -125 C 2 52 C 1 -25 C 1 1 C 1 89 C 2 -137 C 1 -135 C 1 241 C 1 -87 C 2 -187 C 1 196 C 1 -12 C 1 -282 C 2 74 C 1 196 C 1 -124 C 1 -204 C 2 334 C 1 208 C 1 -179 C 1 -3 C 2 105 C 1 -173 C 1 172 C 2 65 C 1 -235 C 1 60 C 1 95 C 2 -14 C 1 -120 C 1 5 C 1 -33 C 2 -99 C 1 354 C 1 -38 C 1 -114 C 2 67 C 1 -21 C 1 152 C 1 7 C 2 -24 C 1 -185 C 1 -93 C 1 40 C 2 52 C 1 -39 C 1 201 C 1 -71 C 2 43 C 1 33 C 1 -159 C 1 148 C 2 93 C 1 11 C 1 -134 C 2 -239 C 1 -21 C 1 127 C 1 -14 C 2 -11 C 1 -74 C 1 199 C 1 79 C 2 -140 C 1 13 C 1 181 C 1 -131 C 2 90 C 1 -59 C 1 -78 C 1 243 C 2 -216 C 1 0 C 1 71 C 1 -20 C 2 151 C 1 58 C 1 -209 C 1 -166 C 2 49 C 1 216 C 1 44 C 1 -382 C 2 -203 C 1 217 C 1 106 C 2 -96 C 1 146 C 1 113 C 1 206 C 2 -192 C 1 18 C 1 24 C 1 -277 C 2 280 C 1 93 C 1 72 C 1 12 C 2 -168 C 1 -28 C 1 -94 C 1 -369 C 2 377 C 1 88 C 1 79 C 1 57 C 2 -224 C 1 46 C 1 79 C 1 98 C 2 127 C 1 -220 C 1 -3 C 1 -4 C 2 161 C 1 78 C 1 -419 C 2 277 C 1 131 C 1 -25 C 1 -164 C 2 64 C 1 128 C 1 -183 C 1 123 C 2 -69 C 1 12 C 1 12 C 1 -150 C 2 254 C 1 -156 C 1 55 C 1 -81 C 2 -509 C 1 286 C 1 178 C 1 -19 C 2 -2 C 1 -11 C 1 143 C 1 28 C 2 -68 C 1 50 C 1 114 C 1 -170 C 2 -273 C 1 170 C 1 223 C 2 -95 C 1 21 C 1 132 C 1 22 C 2 -100 C 1 -76 C 1 7 C 1 153 C 2 45 C 1 -79 C 1 186 C 1 -109 C 2 28 C 1 -161 C 1 -31 C 1 -109 C 2 215 C 1 -168 C 1 -179 C 1 -50 C 2 156 C 1 27 C 1 52 C 1 1 C 2 -26 C 1 -5 C 1 -90 C 2 -98 C 1 -153 C 1 241 C 1 43 C 2 -71 C 1 94 C 1 58 C 1 -18 C 2 -231 C 1 81 C 1 76 C 1 -5 C 2 -275 C 1 77 C 1 223 C 1 65 C 2 -104 C 1 26 C 1 46 C 1 26 C 2 10 C 1 112 C 1 69 C 1 -17 C 2 -45 C 1 -119 C 1 -191 C 1 186 C 2 -131 C 1 154 C 1 121 C 2 224 C 1 -196 C 1 -235 C 1 216 C 2 -86 C 1 -107 C 1 45 C 1 89 C 2 161 C 1 -75 C 1 -324 C 1 149 C 2 96 C 1 -77 C 1 67 C 1 17 C 2 -115 C 1 -143 C 1 110 C 1 149 C 2 56 C 1 -132 C 1 -157 C 1 37 C 2 211 C 1 76 C 1 20 C 1 -151 C 2 18 C 1 -20 C 1 293 C 2 -79 C 1 26 C 1 -35 C 1 -58 C 2 -258 C 1 147 C 1 43 C 1 -42 C 2 78 C 1 -2 C 1 122 C 1 29 C 2 -95 C 1 -36 C 1 -5 C 1 -42 C 2 266 C 1 38 C 1 -68 C 1 59 C 2 -34 C 1 -171 C 1 52 C 1 -17 C 2 112 C 1 -83 C 1 -1 C 1 42 C 2 -13 C 1 -44 C 1 80 C 2 -231 C 1 3 C 1 174 C 1 -95 C 2 132 C 1 205 C 1 47 C 1 -38 C 2 -284 C 1 157 C 1 7 C 1 72 C 2 -6 C 1 15 C 1 -249 C 1 -70 C 2 448 C 1 62 C 1 -421 C 1 76 C 2 18 C 1 -63 C 1 166 C 1 84 C 2 -185 C 1 3 C 1 12 C 1 -16 C 2 -46 C 1 52 C 1 -9 C 2 -66 C 1 -43 C 1 139 C 1 -100 C 2 125 C 1 40 C 1 -66 C 1 119 C 2 -4 C 1 -4 C 1 -11 C 1 -237 C 2 259 C 1 27 C 1 -22 C 1 -133 C 2 -355 C 1 243 C 1 102 C 1 5 C 2 243 C 1 21 C 1 -165 C 1 38 C 2 57 C 1 -69 C 1 -53 C 1 212 C 2 -94 C 1 -193 C 1 58 C 2 66 C 1 -154 C 1 269 C 1 39 C 2 -263 C 1 89 C 1 53 C 1 153 C 2 51 C 1 -209 C 1 -129 C 1 -121 C 2 124 C 1 93 C 1 93 C 1 54 C 2 -81 C 1 122 C 1 33 C 1 -137 C 2 -150 C 1 -332 C 1 91 C 1 489 C 2 -88 C 1 -213 C 1 43 C 2 275 C 1 -144 C 1 -46 C 1 -50 C 2 130 C 1 -81 C 1 -386 C 1 76 C 2 178 C 1 60 C 1 -53 C 1 -168 C 2 160 C 1 42 C 1 -68 C 1 146 C 2 107 C 1 -359 C 1 84 C 1 68 C 2 -95 C 1 -48 C 1 -195 C 1 247 C 2 34 C 1 -132 C 1 -112 C 1 47 C 2 23 C 1 -21 C 1 72 C 2 38 C 1 105 C 1 -109 C 1 236 C 2 -39 C 1 -63 C 1 -39 C 1 20 C 2 -158 C 1 151 C 1 86 C 1 -131 C 2 5 C 1 44 C 1 31 C 1 -35 C 2 -239 C 1 210 C 1 -94 C 1 -163 C 2 155 C 1 97 C 1 -69 C 1 240 C 2 -142 C 1 146 C 1 74 C 1 -87 C 2 53 C 1 65 C 1 -74 C 2 -14 C 1 -63 C 1 -239 C 1 163 C 2 128 C 1 33 C 1 -51 C 1 -25 C 2 177 C 1 -41 C 1 -100 C 1 -147 C 2 187 C 1 22 C 1 132 C 1 -57 C 2 41 C 1 99 C 1 31 C 1 128 C 2 -404 C 1 163 C 1 -47 C 1 243 C 2 89 C 1 -129 C 1 -29 C 1 -103 C 2 -237 C 1 229 C 1 203 C 2 -77 C 1 100 C 1 58 C 1 -94 C 2 -42 C 1 -144 C 1 -84 C 1 193 C 2 110 C 1 -241 C 1 89 C 1 -4 C 2 102 C 1 54 C 1 -248 C 1 -177 C 2 218 C 1 214 C 1 109 C 1 -158 C 2 53 C 1 -5 C 1 -126 C 1 -109 C 2 129 C 1 -130 C 1 -103 C 1 46 C 2 243 C 1 253 C 1 -19 C 2 -265 C 1 78 C 1 -12 C 1 -231 C 2 69 C 1 208 C 1 42 C 1 6 C 2 108 C 1 116 C 1 -19 C 1 -275 C 2 76 C 1 3 C 1 82 C 1 5 C 2 16 C 1 -71 C 1 -9 C 1 71 C 2 3 C 1 99 C 1 -62 C 1 -214 C 2 120 C 1 111 C 1 -65 C 1 99 C 2 -57 C 1 81 C 1 -136 C 2 -15 C 1 -26 C 1 -108 C 1 -115 C 2 0 C 1 -125 C 1 48 C 1 184 C 2 112 C 1 25 C 1 -80 C 1 -185 C 2 -124 C 1 47 C 1 232 C 1 30 C 2 -142 C 1 -43 C 1 87 C 1 44 C 2 45 C 1 -5 C 1 -115 C 1 -211 C 2 95 C 1 222 C 1 -58 C 1 93 C 2 97 C 1 -147 C 1 -215 C 2 49 C 1 23 C 1 -40 C 1 203 C 2 110 C 1 -164 C 1 130 C 1 8 C 2 -115 C 1 35 C 1 -54 C 1 -44 C 2 7 C 1 304 C 1 15 C 1 -215 C 2 60 C 1 -109 C 1 -20 C 1 164 C 2 15 C 1 -133 C 1 15 C 1 79 C 2 16 C 1 -107 C 1 162 C 2 -104 C 1 26 C 1 80 C 1 -154 C 2 -118 C 1 425 C 1 -39 C 1 -114 C 2 184 C 1 -65 C 1 6 C 1 119 C 2 -33 C 1 -28 C 1 171 C 1 80 C 2 -136 C 1 -15 C 1 25 C 1 -21 C 2 26 C 1 -44 C 1 25 C 1 -285 C 2 526 C 1 -12 C 1 -120 C 1 19 C 2 -164 C 1 246 C 1 -32 C 2 -39 C 1 7 C 1 34 C 1 -116 C 2 -97 C 1 21 C 1 117 C 1 -49 C 2 147 C 1 -1 C 1 17 C 1 125 C 2 -115 C 1 -55 C 1 45 C 1 95 C 2 -268 C 1 25 C 1 229 C 1 -16 C 2 -107 C 1 73 C 1 -9 C 1 123 C 2 28 C 1 -149 C 1 24 C 1 53 C 2 117 C 1 -216 C 1 -27 C 2 240 C 1 -47 C 1 -304 C 1 179 C 2 -26 C 1 -123 C 1 152 C 1 5 C 2 49 C 1 -33 C 1 -12 C 1 -15 C 2 74 C 1 40 C 1 -188 C 1 239 C 2 102 C 1 -133 C 1 -297 C 1 -65 C 2 224 C 1 -114 C 1 -88 C 1 -38 C 2 61 C 1 75 C 1 154 C 1 -116 C 2 -256 C 1 131 C 1 -133 C 2 -320 C 1 9 C 1 311 C 1 51 C 2 -59 C 1 159 C 1 -122 C 1 -99 C 2 -38 C 1 117 C 1 -45 C 1 63 C 2 -101 C 1 -151 C 1 18 C 1 186 C 2 235 C 1 -19 C 1 -71 C 1 -134 C 2 42 C 1 -200 C 1 178 C 1 -10 C 2 -232 C 1 194 C 1 -272 C 1 -56 C 2 250 C 1 -53 C 1 -265 C 2 57 C 1 86 C 1 -156 C 1 217 C 2 103 C 1 -26 C 1 31 C 1 -108 C 2 53 C 1 -84 C 1 -197 C 1 256 C 2 81 C 1 -243 C 1 239 C 1 127 C 2 -323 C 1 -78 C 1 20 C 1 17 C 2 -45 C 1 162 C 1 11 C 1 -31 C 2 53 C 1 72 C 1 90 C 1 -238 C 2 -35 C 1 229 C 1 -53 C 2 62 C 1 -91 C 1 -5 C 1 113 C 2 -131 C 1 -16 C 1 25 C 1 173 C 2 -236 C 1 23 C 1 -119 C 1 -57 C 2 96 C 1 -16 C 1 91 C 1 77 C 2 -100 C 1 -64 C 1 -31 C 1 -40 C 2 6 C 1 162 C 1 123 C 1 25 C 2 -173 C 1 -11 C 1 -56 C 1 -40 C 2 73 C 1 -86 C 1 -68 C 2 -45 C 1 117 C 1 -54 C 1 -43 C 2 128 C 1 -103 C 1 14 C 1 92 C 2 -228 C 1 -1 C 1 113 C 1 -14 C 2 72 C 1 -181 C 1 -25 C 1 137 C 2 -131 C 1 -153 C 1 81 C 1 -101 C 2 -26 C 1 18 C 1 0 C 1 26 C 2 -31 C 1 -138 C 1 -52 C 2 69 C 1 49 C 1 21 C 1 -39 C 2 -275 C 1 -347 C 1 -218 C 1 -285 C 2 169 C 1 287 C 1 419 C 1 252 C 2 59 C 1 0 C 1 -90 C 1 -52 C 2 11 C 1 147 C 1 62 C 1 -45 C 2 11 C 1 -23 C 1 26 C 1 75 C 2 -42 C 1 185 C 1 60 C 1 -153 C 2 62 C 1 165 C 1 -44 C 2 -8 C 1 -177 C 1 68 C 1 240 C 2 -110 C 1 4 C 1 91 C 1 -110 C 2 115 C 1 -9 C 1 -109 C 1 -6 C 2 121 C 1 72 C 1 -134 C 1 67 C 2 104 C 1 14 C 1 144 C 1 -31 C 2 -115 C 1 -154 C 1 -30 C 1 64 C 2 2 C 1 120 C 1 43 C 1 -59 C 2 -96 C 1 11 C 1 -116 C 2 64 C 1 160 C 1 -186 C 1 362 C 2 -170 C 1 7 C 1 42 C 1 56 C 2 -101 C 1 15 C 1 128 C 1 -83 C 2 31 C 1 -178 C 1 48 C 1 193 C 2 -90 C 1 -76 C 1 -45 C 1 -13 C 2 18 C 1 -216 C 1 90 C 1 -53 C 2 63 C 1 40 C 1 325 C 1 -104 C 2 -294 C 1 262 C 1 -47 C 2 -239 C 1 155 C 1 109 C 1 -101 C 2 143 C 1 -21 C 1 -14 C 1 -53 C 2 -221 C 1 68 C 1 2 C 1 -23 C 2 196 C 1 46 C 1 -188 C 1 38 C 2 226 C 1 -119 C 1 192 C 1 -25 C 2 -64 C 1 98 C 1 -17 C 1 150 C 2 51 C 1 8 C 1 -213 C 1 -181 C 2 -20 C 1 135 C 1 83 C 2 -92 C 1 83 C 1 -110 C 1 51 C 2 128 C 1 86 C 1 -147 C 1 44 C 2 -60 C 1 -300 C 1 41 C 1 286 C 2 92 C 1 -154 C 1 239 C 1 222 C 2 -195 C 1 -117 C 1 -20 C 1 -17 C 2 29 C 1 244 C 1 -234 C 1 76 C 2 311 C 1 73 C 1 -97 C 1 -179 C 2 150 C 1 -61 C 1 -75 C 2 8 C 1 73 C 1 -5 C 1 -61 C 2 1 C 1 -186 C 1 155 C 1 41 C 2 -150 C 1 263 C 1 33 C 1 -236 C 2 -8 C 1 273 C 1 -166 C 1 -47 C 2 -55 C 1 191 C 1 -34 C 1 -62 C 2 -22 C 1 -47 C 1 98 C 1 9 C 2 -163 C 1 -160 C 1 263 C 2 -25 C 1 -70 C 1 7 C 1 156 C 2 -53 C 1 -36 C 1 5 C 1 -193 C 2 13 C 1 -68 C 1 10 C 1 74 C 2 125 C 1 -31 C 1 -40 C 1 68 C 2 49 C 1 -250 C 1 131 C 1 -10 C 2 108 C 1 3 C 1 -445 C 1 253 C 2 -36 C 1 38 C 1 -40 C 1 1 C 2 32 C 1 12 C 1 78 C 2 -46 C 1 -220 C 1 15 C 1 71 C 2 -84 C 1 35 C 1 -17 C 1 -193 C 2 103 C 1 100 C 1 -417 C 1 94 C 2 139 C 1 -63 C 1 -73 C 1 134 C 2 -113 C 1 71 C 1 -21 C 1 -90 C 2 12 C 1 127 C 1 -39 C 1 -229 C 2 100 C 1 148 C 1 -48 C 1 163 C 2 -57 C 1 -262 C 1 -41 C 2 52 C 1 110 C 1 -62 C 1 86 C 2 15 C 1 -115 C 1 144 C 1 -132 C 2 -185 C 1 51 C 1 14 C 1 -53 C 2 150 C 1 130 C 1 -80 C 1 -71 C 2 80 C 1 -260 C 1 -59 C 1 183 C 2 127 C 1 3 C 1 -51 C 1 -40 C 2 -58 C 1 81 C 1 79 C 1 -54 C 2 -218 C 1 8 C 1 94 C 2 127 C 1 127 C 1 -29 C 1 -105 C 2 -196 C 1 12 C 1 115 C 1 -54 C 2 175 C 1 63 C 1 26 C 1 51 C 2 105 C 1 -101 C 1 27 C 1 -45 C 2 85 C 1 -208 C 1 -58 C 1 249 C 2 -8 C 1 -70 C 1 29 C 1 -89 C 2 52 C 1 -2 C 1 -105 C 1 109 C 2 -69 C 1 -20 C 1 -83 C 2 271 C 1 29 C 1 -134 C 1 -44 C 2 -34 C 1 -75 C 1 -213 C 1 23 C 2 162 C 1 78 C 1 -149 C 1 264 C 2 18 C 1 -258 C 1 -173 C 1 -70 C 2 90 C 1 124 C 1 -37 C 1 22 C 2 108 C 1 44 C 1 -41 C 1 92 C 2 -190 C 1 -131 C 1 -177 C 1 168 C 2 239 C 1 -72 C 1 -91 C 2 -5 C 1 -30 C 1 195 C 1 -131 C 2 -160 C 1 112 C 1 143 C 1 29 C 2 50 C 1 -102 C 1 -9 C 1 67 C 2 -293 C 1 -93 C 1 166 C 1 132 C 2 44 C 1 90 C 1 -112 C 1 -214 C 2 41 C 1 -71 C 1 276 C 1 -107 C 2 -19 C 1 -117 C 1 -68 C 1 97 C 2 -34 C 1 -64 C 1 -244 C 2 153 C 1 126 C 1 44 C 1 -165 C 2 7 C 1 -21 C 1 69 C 1 -141 C 2 -159 C 1 247 C 1 42 C 1 -8 C 2 70 C 1 -120 C 1 -11 C 1 113 C 2 -85 C 1 -167 C 1 180 C 1 -359 C 2 148 C 1 -86 C 1 -149 C 1 203 C 2 27 C 1 -138 C 1 191 C 2 39 C 1 -25 C 1 -62 C 1 37 C 2 117 C 1 -92 C 1 -68 C 1 68 C 2 -23 C 1 -4 C 1 124 C 1 36 C 2 -258 C 1 114 C 1 -119 C 1 0 C 2 -145 C 1 -1 C 1 69 C 1 -41 C 2 67 C 1 152 C 1 -69 C 1 -219 C 2 290 C 1 -20 C 1 -3 C 1 24 C 2 -51 C 1 299 C 1 -135 C 2 -93 C 1 80 C 1 -70 C 1 -177 C 2 166 C 1 70 C 1 -28 C 1 -182 C 2 -95 C 1 361 C 1 98 C 1 -120 C 2 57 C 1 22 C 1 155 C 1 -307 C 2 -115 C 1 291 C 1 110 C 1 -428 C 2 -142 C 1 301 C 1 157 C 1 205 C 2 -76 C 1 -118 C 1 31 C 1 -6 C 2 -32 C 1 -127 C 1 -165 C 2 231 C 1 68 C 1 87 C 1 96 C 2 -152 C 1 -174 C 1 -14 C 1 225 C 2 -39 C 1 -233 C 1 110 C 1 -30 C 2 -85 C 1 221 C 1 87 C 1 -244 C 2 103 C 1 37 C 1 -50 C 1 -45 C 2 164 C 1 -5 C 1 -243 C 1 20 C 2 -105 C 1 -289 C 1 337 C 1 145 C 2 57 C 1 -21 C 1 -414 C 2 394 C 1 -31 C 1 4 C 1 53 C 2 -113 C 1 -33 C 1 -4 C 1 -71 C 2 64 C 1 -115 C 1 38 C 1 69 C 2 -34 C 1 -23 C 1 29 C 1 33 C 2 2 C 1 -20 C 1 189 C 1 -70 C 2 -188 C 1 92 C 1 -84 C 1 -50 C 2 442 C 1 -42 C 1 -442 C 1 25 C 2 262 C 1 -16 C 1 -3 C 2 -83 C 1 -8 C 1 -174 C 1 313 C 2 50 C 1 -38 C 1 -202 C 1 -117 C 2 77 C 1 -169 C 1 -15 C 1 230 C 2 -24 C 1 5 C 1 -24 C 1 -3 C 2 -38 C 1 96 C 1 -94 C 1 13 C 2 -43 C 1 162 C 1 57 C 1 -76 C 2 72 C 1 -70 C 1 -214 C 1 41 C 2 -15 C 1 24 C 1 89 C 2 -30 C 1 -82 C 1 13 C 1 -90 C 2 20 C 1 -87 C 1 -109 C 1 251 C 2 34 C 1 54 C 1 42 C 1 22 C 2 -341 C 1 -7 C 1 98 C 1 122 C 2 -43 C 1 -61 C 1 -115 C 1 -138 C 2 189 C 1 96 C 1 -68 C 1 -190 C 2 -78 C 1 186 C 1 114 C 1 -63 C 2 -68 C 1 99 C 1 -106 C 2 -112 C 1 295 C 1 81 C 1 -121 C 2 -133 C 1 -59 C 1 150 C 1 53 C 2 -279 C 1 303 C 1 204 C 1 -222 C 2 -97 C 1 -147 C 1 103 C 1 -200 C 2 212 C 1 78 C 1 68 C 1 -13 C 2 -26 C 1 -128 C 1 2 C 1 -86 C 2 -35 C 1 29 C 1 126 C 2 -93 C 1 -233 C 1 -123 C 1 326 C 2 -3 C 1 -50 C 1 -103 C 1 222 C 2 17 C 1 -30 C 1 -69 C 1 33 C 2 -11 C 1 -237 C 1 47 C 1 191 C 2 58 C 1 -1 C 1 -22 C 1 -11 C 2 13 C 1 54 C 1 -156 C 1 -25 C 2 210 C 1 145 C 1 -131 C 1 46 C 2 -25 C 1 193 C 1 -2 C 2 50 C 1 -147 C 1 92 C 1 -73 C 2 -116 C 1 -46 C 1 125 C 1 62 C 2 -83 C 1 -101 C 1 -36 C 1 148 C 2 -226 C 1 -107 C 1 226 C 1 132 C 2 -101 C 1 -21 C 1 63 C 1 -39 C 2 -132 C 1 -47 C 1 39 C 1 -31 C 2 -140 C 1 -272 C 1 486 C 1 106 C 2 29 C 1 56 C 1 -276 C 2 160 C 1 -16 C 1 37 C 1 24 C 2 -61 C 1 141 C 1 -93 C 1 -89 C 2 116 C 1 33 C 1 -91 C 1 -224 C 2 322 C 1 15 C 1 -130 C 1 17 C 2 -53 C 1 147 C 1 -107 C 1 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C 1 0 C 1 0 C 1 0 C 1 0 C 1 -1 C 1 0 C 1 0 C 1 0 C 1 -1 C 0 2 C 1 0 C 1 0 C 1 1 C 1 1 C 1 2 C 0 4 C 1 13 C 0 -32 C 0 1 8476 742 L 1 0 C 1 1 C 1 0 C 1 0 C 1 0 C 1 0 C 1 0 C 1 0 C 1 0 C 1 0 C 1 0 C 1 0 C 1 0 C 1 0 C 1 -1 C 1 0 C 1 0 C 1 0 C 1 -1 C 1 5 8500 742 L 0 -3 C 1 -1 C 1 0 C 1 -1 C 0 1 8531 742 L 1 1 C 0 2 C 1 4 C 1 12 C 1 77 C 1 -97 C 1 186 8598 742 L 1 -183 C 0 -3 C 0 77 8662 742 L 1 -71 C 1 -6 C 0 92 8725 742 L 1 -92 C 0 204 8887 742 L 1 -204 C 0 48 9176 742 L 0 -48 C 0.000 setgray PGPLOT restore showpage %%PageTrailer %%PageBoundingBox: 78 93 553 712 %%Trailer %%BoundingBox: 78 93 553 712 %%DocumentFonts: %%Pages: 1 %%EOF %%EndDocument @endspecial 415 5033 a Fn(Figure)45 b(8.)68 b Fm(The)39 b(sp)s(ectrum)g(for)h(the)f(mo)s(del)f(of)i(three)g(rotators,)h(for)f (the)g(ordered)415 5142 y(motions)29 b(whic)m(h)i(tak)m(e)f(place)h(in) f(the)h(inner)f(part)h(of)g(a)g(resonance,)g(at)f Fl(")c Fm(=)f(10)3161 5104 y Fk(\000)p Fj(4)3260 5142 y Fm(.)41 b(The)415 5252 y(detail)30 b(on)h(the)f(righ)m(t)h(sho)m(ws)h(that)f (bands)g(are)g(no)m(w)g(resolv)m(ed)g(in)m(to)g(lines.)1900 5579 y Fy(16)p eop %%Page: 17 17 17 16 bop 0 100 a Ft(C.)34 b(Motions)j(in)f(the)g(inner)h(pa)m(rt)f(of) f(resonances.)101 b Fy(F)-8 b(or)35 b(the)g(sak)m(e)h(of)f (completeness,)h(w)m(e)f(presen)m(t)i(here)0 219 y(some)32 b(further)i(results)f(concerning)g(the)g(sp)s(ectrum)g(of)f(resonan)m (t)i(motions)d(whic)m(h)i(tak)m(e)f(place)h(in)g(the)0 339 y(inner)44 b(part)g(of)g(the)g(resonan)m(t)h(domains.)75 b(Consider)45 b(again)e(the)h(Hamiltonian)e Fr(K)3220 354 y Fo(0)3308 339 y Fy(in)m(tro)s(duced)j(in)0 458 y(\(2.14\),)h(and)g(let)f(\()p Fs(')796 422 y Fg(\003)796 483 y Fq(m)p Fo(+1)972 458 y Fs(;)17 b(:)g(:)g(:)d(;)j(')1259 422 y Fg(\003)1259 483 y Fq(n)1313 458 y Fy(\))45 b(b)s(e)g(a)g(minim)m (um)e(of)i(the)g(p)s(oten)m(tial)g Fs(g)t Fy(\()p Fs(')2994 473 y Fq(m)p Fo(+1)3169 458 y Fs(;)17 b(:)g(:)g(:)d(;)j(')3456 473 y Fq(n)3510 458 y Fy(\).)79 b(Quite)0 578 y(clearly)-8 b(,)33 b(the)i(Hamiltonian)d Fr(K)1162 593 y Fo(0)1241 578 y Fy(has)j(an)f(elliptic)g(equilibrium)f(in)h(\(0)p Fs(;)17 b(:)g(:)g(:)d(;)j Fy(0)p Fs(;)g(')3005 542 y Fg(\003)3005 603 y Fq(m)p Fo(+1)3180 578 y Fs(;)g(:)g(:)g(:)d(;)j(') 3467 542 y Fg(\003)3467 602 y Fq(n)3521 578 y Fy(\),)34 b(and)h(in)0 697 y(a)f(su\016cien)m(tly)g(small)e(neigh)m(b)s(orho)s(o) s(d)i(of)g(this)g(p)s(oin)m(t)g(most)f(motions)f(\(for)i(KAM)g (theorem,)f(whic)m(h)i(is)0 817 y(kno)m(wn)30 b(to)g(hold)g(in)g (general)g(assumptions)g(around)h(elliptic)e(equilibria\))g(are)h (quasi)g(p)s(erio)s(dic.)43 b(As)30 b(far)0 936 y(as)25 b(the)h(heuristic)g(argumen)m(t)f(sk)m(etc)m(hed)h(in)g(Section)f(2C)g (is)h(reliable,)g(the)f(original)g(Hamiltonian)d(\(2.12\))0 1056 y(is)29 b(also)f(exp)s(ected)h(to)g(exhibit)f(quasi-p)s(erio)s (dic)h(motions.)41 b(These)30 b(regular)e(motions)g(tak)m(e)g(place)h (in)g(the)0 1176 y(inner)37 b(part)g(of)g(a)f(resonance)i(|)f(the)g (scaled)g(actions)g Fs(J)46 b Fy(sta)m(y)37 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2 38 C 3 -112 C 3 -115 C 2 31 C 3 -68 C 3 77 C 3 234 C 2 -108 C 3 -329 C 3 -10 C 2 -48 C 3 -57 C 3 148 C 2 122 C 3 75 C 3 -91 C 2 -36 C 3 -16 C 3 52 C 2 73 C 3 168 C 3 -160 C 2 -94 C 3 87 C 3 22 C 3 57 C 2 -63 C 3 -184 C 3 108 C 2 81 C 3 -20 C 3 -35 C 2 -5 C 3 98 C 3 -25 C 2 -192 C 3 -67 C 3 37 C 2 96 C 3 111 C 3 -105 C 2 -222 C 3 234 C 3 131 C 3 -3 C 2 46 C 3 -91 C 3 -40 C 2 218 C 3 -131 C 3 -222 C 2 163 C 3 116 C 3 6 C 2 -132 C 3 -54 C 3 219 C 2 82 C 3 -194 C 3 -129 C 2 113 C 3 19 C 3 30 C 3 163 C 2 71 C 3 -156 C 3 -21 C 2 -11 C 3 109 C 3 27 C 2 -102 C 3 55 C 3 89 C 2 -57 C 3 47 C 3 50 C 2 188 C 3 -127 C 3 -235 C 2 101 C 3 27 C 3 199 C 3 32 C 2 -70 C 3 -400 C 3 454 C 2 129 C 3 -273 C 3 1 C 2 14 C 3 149 C 3 40 C 2 -172 C 3 -66 C 3 105 C 2 -13 C 3 27 C 3 -50 C 2 36 C 3 72 C 3 -63 C 3 -11 C 2 301 C 3 -576 C 3 472 C 2 -2 C 3 117 C 3 -65 C 2 -40 C 3 119 C 3 2 C 2 -206 C 3 216 C 3 -248 C 2 236 C 3 158 C 3 -2 C 2 -286 C 3 109 C 3 289 C 3 -14 C 2 -104 C 3 -146 C 3 114 C 2 -47 C 3 64 C 3 -113 C 2 -85 C 3 76 C 3 17 C 2 -95 C 3 -101 C 3 -378 C 2 9 C 3 318 C 3 4 C 2 -122 C 3 -21 C 3 1 C 3 -95 C 2 -30 C 3 14 C 3 -69 C 2 43 C 3 81 C 3 -52 C 2 48 C 3 -76 C 3 -72 C 2 -45 C 3 205 C 3 111 C 2 -50 C 3 45 C 3 10 C 2 -32 C 3 8 C 3 70 C 3 9 C 2 -13 C 3 76 C 3 -3 C 2 158 C 3 9 C 3 -64 C 2 86 C 3 91 C 3 175 C 2 -63 C 3 -162 C 3 105 C 2 -72 C 3 -90 C 3 -13 C 2 27 C 3 -39 C 3 76 C 3 95 C 2 -90 C 3 -52 C 3 3 C 2 -25 C 3 -78 C 3 37 C 2 39 C 3 -143 C 3 110 C 2 -52 C 3 77 C 3 -150 C 2 -27 C 3 -75 C 3 -225 C 2 -7 C 3 119 C 3 6 C 3 -154 C 2 155 C 3 24 C 3 1 C 2 47 C 3 -41 C 3 157 C 2 134 C 3 -262 C 3 -4 C 2 -16 C 3 89 C 3 -74 C 2 73 C 3 25 C 3 -177 C 2 -180 C 3 187 C 3 70 C 3 -31 C 2 -55 C 3 -257 C 3 -119 C 2 268 C 3 46 C 3 101 C 2 -2 C 3 77 C 3 -47 C 2 -237 C 3 -236 C 3 231 C 2 82 C 3 26 C 3 -212 C 2 -141 C 3 -27 C 3 114 C 3 -75 C 2 187 C 3 -108 C 3 -125 C 2 -25 C 3 29 C 3 413 C 2 -154 C 3 -84 C 3 31 C 2 98 C 3 67 C 3 -192 C 2 0 C 3 27 C 3 36 C 2 39 C 3 53 C 3 -61 C 3 -74 C 2 -141 C 3 405 C 3 2 C 2 -388 C 3 -36 C 3 54 C 2 142 C 3 -10 C 3 -66 C 2 43 C 3 23 C 3 -78 C 2 -8 C 3 243 C 3 -43 C 2 -252 C 3 196 C 3 53 C 3 57 C 2 170 C 3 -65 C 3 8 C 2 -148 C 3 -7 C 3 -154 C 2 133 C 3 116 C 3 -29 C 2 161 C 3 -54 C 3 -217 C 2 158 C 3 138 C 3 -71 C 2 131 C 3 55 C 3 -232 C 3 -30 C 2 159 C 3 133 C 3 -74 C 2 -43 C 3 -41 C 3 -120 C 2 -21 C 3 -29 C 3 126 C 2 -53 C 3 9 C 3 -9 C 2 -70 C 3 238 C 3 96 C 2 -65 C 3 213 C 3 10 C 3 -119 C 2 -44 C 3 178 C 3 -91 C 2 -2 C 3 62 C 3 -44 C 2 9 C 3 113 C 3 51 C 2 -94 C 3 -27 C 3 -70 C 2 22 C 3 110 C 3 91 C 2 -42 C 3 -162 C 3 268 C 3 27 C 2 -213 C 3 51 C 3 -2 C 2 -200 C 3 73 C 3 -16 C 2 -146 C 3 87 C 3 -44 C 2 -182 C 3 -65 C 3 135 C 2 -137 C 3 9 C 3 28 C 2 111 C 3 -270 C 3 -7 C 3 14 C 2 -79 C 3 -212 C 3 248 C 2 -11 C 3 69 C 3 191 C 2 -93 C 3 -36 C 3 73 C 2 -30 C 3 0 C 3 84 C 2 42 C 3 35 C 3 -316 C 2 175 C 3 159 C 3 159 C 3 138 C 2 20 C 3 -149 C 3 184 C 2 108 C 3 -67 C 3 -152 C 2 44 C 3 75 C 3 79 C 2 -8 C 3 -331 C 3 49 C 2 181 C 3 24 C 3 -248 C 2 137 C 3 -101 C 3 -129 C 3 220 C 2 -77 C 3 -67 C 3 18 C 2 19 C 3 35 C 3 -103 C 2 107 C 3 16 C 3 -332 C 2 -16 C 3 19 C 3 -18 C 2 64 C 3 0 C 3 -149 C 2 -14 C 3 32 C 3 113 C 3 131 C 2 -106 C 3 -205 C 3 61 C 2 62 C 3 235 C 3 -34 C 2 -310 C 3 152 C 3 52 C 2 -81 C 3 -164 C 3 62 C 2 -94 C 3 176 C 3 26 C 2 -171 C 3 82 C 3 -146 C 3 94 C 2 37 C 3 36 C 3 -33 C 2 -130 C 3 -83 C 3 24 C 2 7 C 3 108 C 3 -61 C 2 -145 C 3 -12 C 3 -14 C 2 9 C 3 44 C 3 94 C 2 -76 C 3 -105 C 3 -5 C 3 37 C 2 -121 C 3 -26 C 3 32 C 2 242 C 3 -88 C 3 -42 C 2 52 C 3 -102 C 3 50 C 2 -117 C 3 -200 C 3 -82 C 2 336 C 3 -47 C 3 -100 C 2 12 C 3 -7 C 3 133 C 3 115 C 2 -4 C 3 -81 C 3 -163 C 2 66 C 3 -33 C 3 -120 C 2 -101 C 3 361 C 3 64 C 2 -136 C 3 87 C 3 -92 C 2 27 C 3 113 C 3 -67 C 2 50 C 3 -8 C 3 -118 C 3 -130 C 2 112 C 3 -70 C 3 -161 C 2 -57 C 3 -28 C 3 184 C 2 -22 C 3 121 C 3 137 C 2 -55 C 3 -46 C 3 40 C 2 -156 C 3 151 C 3 76 C 2 84 C 3 -44 C 3 -181 C 3 12 C 2 76 C 3 -57 C 3 -154 C 2 119 C 3 -54 C 3 -24 C 2 156 C 3 -82 C 3 41 C 2 189 C 3 19 C 3 77 C 2 -27 C 3 -5 C 3 -44 C 2 -18 C 3 69 C 3 185 C 3 -66 C 2 -95 C 3 94 C 3 54 C 2 -306 C 3 157 C 3 162 C 2 13 C 3 -45 C 3 -15 C 2 -168 C 3 -41 C 3 251 C 2 217 C 3 -227 C 3 -131 C 2 67 C 3 -121 C 3 196 C 3 29 C 2 -385 C 3 228 C 3 26 C 2 -181 C 3 27 C 3 -22 C 2 -260 C 3 231 C 3 72 C 2 -140 C 3 -152 C 3 69 C 2 -91 C 3 42 C 3 68 C 2 -181 C 3 67 C 3 -13 C 3 23 C 2 -153 C 3 162 C 3 116 C 2 99 C 3 -66 C 3 22 C 2 4 C 3 -68 C 3 166 C 2 -203 C 3 -22 C 3 61 C 2 50 C 3 152 C 3 40 C 2 113 C 3 152 C 3 -259 C 3 -80 C 2 229 C 3 -1 C 3 -90 C 2 281 C 3 20 C 3 -126 C 2 -39 C 3 -36 C 3 54 C 2 -212 C 3 -79 C 3 9 C 2 90 C 3 94 C 3 -94 C 2 -30 C 3 -36 C 3 38 C 3 -46 C 2 -182 C 3 236 C 3 -131 C 2 84 C 3 109 C 3 -88 C 2 -171 C 3 -172 C 3 158 C 2 -19 C 3 -180 C 3 51 C 2 171 C 3 -71 C 3 16 C 2 -68 C 3 -46 C 3 142 C 3 22 C 2 11 C 3 28 C 3 -60 C 2 -69 C 3 41 C 3 -8 C 2 -130 C 3 109 C 3 -81 C 2 -157 C 3 343 C 3 -135 C 2 31 C 3 -69 C 3 -165 C 2 130 C 3 -71 C 3 -115 C 3 23 C 2 123 C 3 27 C 3 4 C 2 -29 C 3 -152 C 3 81 C 2 -68 C 3 -209 C 3 69 C 2 194 C 3 37 C 3 -132 C 2 -12 C 3 74 C 3 -34 C 2 -161 C 3 114 C 3 8 C 3 -79 C 2 178 C 3 113 C 3 -201 C 2 5 C 3 38 C 3 404 C 2 629 C 3 200 C 3 135 C 2 216 C 3 -177 C 3 -57 C 2 48 C 3 -558 C 3 -663 C 2 -134 C 3 -111 C 3 -7 C 3 -36 C 2 56 C 3 -99 C 3 144 C 2 -80 C 3 111 C 3 79 C 2 -45 C 3 -240 C 3 56 C 2 89 C 3 -104 C 3 257 C 2 -113 C 3 -40 C 3 61 C 2 -195 C 3 170 C 3 55 C 3 -92 C 2 58 C 3 28 C 3 -250 C 2 -179 C 3 122 C 3 76 C 2 155 C 3 -66 C 3 -21 C 2 151 C 3 -56 C 3 60 C 2 -139 C 3 83 C 3 -79 C 2 151 C 3 -99 C 3 45 C 3 61 C 2 -14 C 3 -14 C 3 -55 C 2 -50 C 3 114 C 3 25 C 2 -77 C 3 71 C 3 73 C 2 -18 C 3 -77 C 3 -26 C 2 14 C 3 7 C 3 96 C 2 -88 C 3 79 C 3 -14 C 3 -46 C 2 152 C 3 -51 C 3 -3 C 2 -11 C 3 -164 C 3 8 C 2 96 C 3 -20 C 3 68 C 2 97 C 3 -48 C 3 -182 C 2 -40 C 3 -123 C 3 79 C 2 183 C 3 47 C 3 -35 C 3 -58 C 2 95 C 3 9 C 3 -163 C 2 40 C 3 -38 C 3 96 C 2 147 C 3 52 C 3 72 C 2 74 C 3 23 C 3 -49 C 2 -198 C 3 50 C 3 -32 C 2 -157 C 3 119 C 3 -133 C 3 24 C 2 73 C 3 101 C 3 143 C 2 -61 C 3 72 C 3 -132 C 2 -62 C 3 -279 C 3 143 C 2 187 C 3 81 C 3 -132 C 2 -238 C 3 -333 C 3 406 C 2 -61 C 3 -93 C 3 339 C 3 75 C 2 -58 C 3 -70 C 3 63 C 2 -9 C 3 -101 C 3 -103 C 2 2 C 3 160 C 3 31 C 2 -100 C 3 112 C 3 -38 C 2 47 C 3 -22 C 3 143 C 2 100 C 3 -158 C 3 -218 C 3 272 C 2 175 C 3 38 C 3 -198 C 2 -156 C 3 105 C 3 -121 C 2 87 C 3 109 C 3 -227 C 2 -18 C 3 241 C 3 72 C 2 -7 C 3 -70 C 3 -222 C 2 201 C 3 34 C 3 -23 C 3 -161 C 2 24 C 3 69 C 3 54 C 2 -86 C 3 -127 C 3 70 C 2 107 C 3 137 C 3 67 C 2 -25 C 3 -224 C 3 2 C 2 169 C 3 -160 C 3 11 C 2 7 C 3 91 C 3 50 C 3 -209 C 2 113 C 3 25 C 3 -125 C 2 214 C 3 80 C 3 -118 C 2 -180 C 3 239 C 3 104 C 2 31 C 3 -178 C 3 -54 C 2 -109 C 3 -187 C 3 193 C 2 14 C 3 82 C 3 78 C 3 -123 C 2 93 C 3 -74 C 3 -7 C 2 270 C 3 507 C 3 1063 C 2 59 C 3 -1001 C 3 -871 C 2 103 C 3 -148 C 3 -117 C 2 48 C 3 79 C 3 167 C 2 -6 C 3 -308 C 3 3 C 3 135 C 2 91 C 3 -96 C 3 224 C 2 -367 C 3 316 C 3 -9 C 2 -198 C 3 164 C 3 119 C 2 -197 C 3 -155 C 3 120 C 2 -57 C 3 156 C 3 -26 C 2 -70 C 3 -161 C 3 -68 C 3 290 C 2 -84 C 3 -9 C 3 134 C 2 32 C 3 1 C 3 -194 C 2 49 C 3 -64 C 3 -69 C 2 80 C 3 201 C 3 -143 C 2 -215 C 3 139 C 3 105 C 2 7 C 3 -175 C 3 135 C 3 -59 C 2 163 C 3 3 C 3 -185 C 2 -159 C 3 226 C 3 89 C 2 -74 C 3 -87 C 3 -198 C 2 129 C 3 352 C 3 111 C 2 -228 C 3 -183 C 3 77 C 2 24 C 3 26 C 3 16 C 3 -301 C 2 -167 C 3 275 C 3 -74 C 2 91 C 3 -53 C 3 -156 C 2 -131 C 3 207 C 3 17 C 2 122 C 3 -8 C 3 -20 C 2 127 C 3 -30 C 3 -194 C 2 -228 C 3 198 C 3 -65 C 3 -358 C 2 501 C 3 149 C 3 -7 C 2 -123 C 3 -37 C 3 -3 C 2 180 C 3 -7 C 3 -77 C 2 -57 C 3 200 C 3 -197 C 2 0 C 3 -9 C 3 -15 C 2 -61 C 3 -151 C 3 160 C 3 48 C 2 162 C 3 41 C 3 -43 C 2 107 C 3 -49 C 3 -214 C 2 -82 C 3 21 C 3 -106 C 2 -146 C 3 182 C 3 100 C 2 1 C 3 -17 C 3 -1 C 2 -24 C 3 -28 C 3 -132 C 3 -66 C 2 0 C 3 133 C 3 -24 C 2 0 C 3 10 C 3 24 C 2 11 C 3 -66 C 3 -23 C 2 131 C 3 172 C 3 -30 C 2 -101 C 3 -252 C 3 70 C 2 198 C 3 90 C 3 -129 C 3 -22 C 2 -160 C 3 -77 C 3 251 C 2 59 C 3 -166 C 3 -120 C 2 38 C 3 103 C 3 -6 C 2 -150 C 3 -125 C 3 246 C 2 66 C 3 32 C 3 -243 C 2 4 C 3 196 C 3 -165 C 3 6 C 2 26 C 3 -107 C 3 178 C 2 -36 C 3 -377 C 3 305 C 2 -27 C 3 56 C 3 -156 C 2 90 C 3 56 C 3 -52 C 2 43 C 3 0 C 3 -84 C 2 -207 C 3 261 C 3 100 C 3 -48 C 2 -74 C 3 -57 C 3 91 C 2 -20 C 3 -70 C 3 0 C 2 121 C 3 -226 C 3 -81 C 2 92 C 3 189 C 3 -81 C 2 -32 C 3 -70 C 3 192 C 2 235 C 3 -21 C 3 35 C 3 587 C 2 761 C 3 39 C 3 100 C 2 -96 C 3 -214 C 3 -279 C 2 -788 C 3 -157 C 3 -54 C 2 -47 C 3 -126 C 3 -82 C 2 -227 C 3 -12 C 3 169 C 2 102 C 3 -154 C 3 139 C 3 0 C 2 -345 C 3 201 C 3 24 C 2 3 C 3 -138 C 3 134 C 2 -58 C 3 -80 C 3 69 C 2 -26 C 3 -4 C 3 -112 C 2 251 C 3 162 C 3 -252 C 2 128 C 3 105 C 3 30 C 3 -399 C 2 206 C 3 75 C 3 -231 C 2 -26 C 3 103 C 3 66 C 2 -86 C 3 -56 C 3 -228 C 2 423 C 3 -7 C 3 -352 C 2 -239 C 3 360 C 3 -112 C 2 202 C 3 66 C 3 121 C 3 43 C 2 -71 C 3 -1 C 3 -182 C 2 -99 C 3 -75 C 3 178 C 2 98 C 3 54 C 3 -63 C 2 -152 C 3 310 C 3 -34 C 2 38 C 3 -24 C 3 -6 C 2 -70 C 3 -98 C 3 -93 C 3 -181 C 2 409 C 3 171 C 3 -84 C 2 -176 C 3 180 C 3 71 C 2 -110 C 3 34 C 3 -29 C 2 -123 C 3 -152 C 3 194 C 2 -51 C 3 -63 C 3 -23 C 2 -135 C 3 213 C 3 -18 C 3 82 C 2 39 C 3 -104 C 3 44 C 2 29 C 3 -35 C 3 -197 C 2 44 C 3 55 C 3 -85 C 2 254 C 3 6 C 3 -178 C 2 10 C 3 173 C 3 -137 C 2 32 C 3 88 C 3 -57 C 3 -118 C 2 41 C 3 48 C 3 -39 C 2 -47 C 3 129 C 3 -218 C 2 30 C 3 95 C 3 78 C 2 -25 C 3 88 C 3 -134 C 2 -142 C 3 214 C 3 148 C 2 -109 C 3 0 C 3 -18 C 3 -70 C 2 201 C 3 -70 C 3 -198 C 2 267 C 3 6 C 3 -181 C 2 200 C 3 -186 C 3 -67 C 2 24 C 3 185 C 3 22 C 2 -62 C 3 211 C 3 -26 C 2 -87 C 3 104 C 3 -46 C 3 -215 C 2 32 C 3 -6 C 3 -51 C 2 -125 C 3 27 C 3 78 C 2 57 C 3 -7 C 3 18 C 2 3 C 3 -117 C 3 26 C 2 49 C 3 -27 C 3 142 C 2 -8 C 3 -228 C 3 41 C 3 47 C 2 4 C 3 -225 C 3 181 C 2 79 C 3 -83 C 3 172 C 2 -143 C 3 221 C 3 43 C 2 -179 C 3 31 C 3 -51 C 2 -18 C 3 29 C 3 -44 C 2 222 C 3 -11 C 3 102 C 3 -3 C 2 54 C 3 -373 C 3 133 C 2 28 C 3 -93 C 3 20 C 2 148 C 3 8 C 3 -148 C 2 -20 C 3 237 C 3 -160 C 2 -227 C 3 359 C 3 -23 C 2 -131 C 3 184 C 3 119 C 3 18 C 2 -52 C 3 18 C 3 -56 C 2 -22 C 3 -187 C 3 194 C 2 -76 C 3 22 C 3 52 C 2 -251 C 3 -48 C 3 120 C 2 203 C 3 2 C 3 -130 C 2 -62 C 3 115 C 3 161 C 3 -50 C 2 -68 C 3 -128 C 3 173 C 2 -44 C 3 143 C 3 65 C 2 -278 C 3 208 C 3 57 C 2 -44 C 3 89 C 3 -78 C 2 -63 C 3 41 C 3 -28 C 2 20 C 3 9 C 3 120 C 3 -147 C 2 20 C 3 38 C 3 99 C 2 87 C 3 66 C 3 -65 C 2 -79 C 3 188 C 3 -74 C 2 -74 C 3 -56 C 3 -182 C 2 330 C 3 70 C 3 -177 C 2 -36 C 3 -14 C 3 -56 C 3 -61 C 2 117 C 3 151 C 3 -46 C 2 63 C 3 192 C 3 -108 C 2 -182 C 3 31 C 3 137 C 2 171 C 3 -305 C 3 90 C 2 112 C 3 -68 C 3 95 C 2 16 C 3 -238 C 3 210 C 3 221 C 2 -106 C 3 -206 C 3 6 C 2 319 C 3 -33 C 3 -10 C 2 -68 C 3 -150 C 3 89 C 2 20 C 3 -5 C 3 -126 C 2 134 C 3 -57 C 3 -59 C 2 -234 C 3 -297 C 3 134 C 3 331 C 2 -121 C 3 -85 C 3 62 C 2 -13 C 3 32 C 3 -36 C 2 -189 C 3 91 C 3 -34 C 2 23 C 3 -178 C 3 230 C 2 -186 C 3 -123 C 3 357 C 2 95 C 3 -183 C 3 -50 C 3 150 C 2 -39 C 3 -61 C 3 168 C 2 -66 C 3 134 C 3 64 C 2 -101 C 3 -19 C 3 129 C 2 140 C 3 -53 C 3 -218 C 2 275 C 3 205 C 3 -48 C 2 -75 C 3 -35 C 3 -88 C 3 0 C 2 56 C 3 -19 C 3 20 C 2 -141 C 3 138 C 3 17 C 2 -173 C 3 12 C 3 60 C 2 -116 C 3 59 C 3 -263 C 2 228 C 3 -8 C 3 -70 C 2 198 C 3 -99 C 3 -81 C 3 -153 C 2 -192 C 3 -2 C 3 79 C 2 -3 C 3 -65 C 3 105 C 2 22 C 3 87 C 3 -19 C 2 -131 C 3 217 C 3 32 C 2 -173 C 3 158 C 3 -80 C 2 -10 C 3 -52 C 3 4 C 3 74 C 2 -114 C 3 -102 C 3 122 C 2 24 C 3 -68 C 3 -3 C 2 -251 C 3 -104 C 3 178 C 2 192 C 3 -96 C 3 23 C 2 101 C 3 -61 C 3 -199 C 2 -157 C 3 123 C 3 193 C 3 -85 C 2 -31 C 3 -158 C 3 117 C 2 -175 C 3 154 C 3 135 C 2 -149 C 3 95 C 3 19 C 2 -65 C 3 66 C 3 68 C 2 33 C 3 -75 C 3 -102 C 2 -39 C 3 31 C 3 147 C 3 -126 C 2 5 C 3 -54 C 3 34 C 2 35 C 3 -99 C 3 23 C 2 208 C 3 -101 C 3 -109 C 2 -89 C 3 142 C 3 56 C 2 -53 C 3 6 C 3 24 C 2 -61 C 3 -1 C 3 -107 C 3 236 C 2 -72 C 3 -222 C 3 285 C 2 1 C 3 9 C 3 82 C 2 -8 C 3 -1 C 3 -243 C 2 35 C 3 82 C 3 87 C 2 102 C 3 -18 C 3 106 C 2 -107 C 3 -99 C 3 47 C 3 55 C 2 75 C 3 117 C 3 -2 C 2 -60 C 3 -116 C 3 119 C 2 -53 C 3 110 C 3 -82 C 2 13 C 3 -51 C 3 -336 C 2 153 C 3 131 C 3 0 C 2 4 C 3 -97 C 3 -128 C 3 535 C 2 -55 C 3 -163 C 3 265 C 2 -31 C 3 -185 C 3 37 C 2 223 C 3 -151 C 3 42 C 2 53 C 3 -7 C 3 -43 C 2 99 C 3 176 C 3 -234 C 2 0 C 3 -20 C 3 63 C 3 182 C 2 -10 C 3 -84 C 3 -138 C 2 329 C 3 -38 C 3 -346 C 2 135 C 3 56 C 3 -286 C 2 72 C 3 -201 C 3 4 C 2 219 C 3 24 C 3 -272 C 2 44 C 3 -65 C 3 -13 C 3 -65 C 2 236 C 3 -29 C 3 -240 C 2 33 C 3 7 C 3 -265 C 2 -226 C 3 254 C 3 -15 C 2 190 C 3 126 C 3 -9 C 2 -5 C 3 78 C 3 -77 C 2 11 C 3 60 C 3 157 C 3 -40 C 2 -96 C 3 -2 C 3 39 C 2 176 C 3 133 C 3 -7 C 2 -96 C 3 25 C 3 253 C 2 -58 C 3 -218 C 3 170 C 2 -63 C 3 115 C 3 -154 C 2 -139 C 3 -71 C 3 333 C 3 -69 C 2 -129 C 3 34 C 3 -33 C 2 -63 C 3 17 C 3 22 C 2 -51 C 3 98 C 3 -91 C 2 12 C 3 -28 C 3 48 C 2 27 C 3 -111 C 3 -77 C 2 -312 C 3 102 C 3 162 C 3 -10 C 2 -396 C 3 76 C 3 47 C 2 296 C 3 75 C 3 -67 C 2 -144 C 3 -1 C 3 -134 C 2 370 C 3 -15 C 3 -165 C 2 77 C 3 -16 C 3 -139 C 2 -36 C 3 -31 C 3 -71 C 3 232 C 2 -175 C 3 -28 C 3 64 C 2 -170 C 3 83 C 3 92 C 2 60 C 3 -37 C 3 -200 C 2 -79 C 3 37 C 3 86 C 2 -63 C 3 42 C 3 -34 C 2 -184 C 3 108 C 3 -9 C 3 -38 C 2 -50 C 3 63 C 3 -180 C 2 146 C 3 58 C 3 -43 C 2 67 C 3 69 C 3 -39 C 2 -84 C 3 169 C 3 -1 C 2 -138 C 3 -90 C 3 92 C 2 -3 C 3 -246 C 3 66 C 3 219 C 2 111 C 3 -199 C 3 -237 C 2 93 C 3 266 C 3 -172 C 2 52 C 3 106 C 3 -74 C 2 -396 C 3 128 C 3 122 C 2 5 C 3 -134 C 3 211 C 2 47 C 3 -327 C 3 -2 C 3 303 C 2 -211 C 3 -357 C 3 190 C 2 213 C 3 -10 C 3 -296 C 2 11 C 3 49 C 3 180 C 2 35 C 3 -57 C 3 34 C 2 114 C 3 -25 C 3 -169 C 2 -93 C 3 -107 C 3 169 C 3 86 C 2 -17 C 3 108 C 3 49 C 2 -68 C 3 -44 C 3 -178 C 2 165 C 3 6 C 3 -141 C 2 6 C 3 56 C 3 69 C 2 -141 C 3 337 C 3 -235 C 2 -50 C 3 135 C 3 -96 C 3 110 C 2 97 C 3 -210 C 3 -152 C 2 366 C 3 -1 C 3 -5 C 2 -34 C 3 -138 C 3 -92 C 2 166 C 3 63 C 3 69 C 2 78 C 3 -168 C 3 33 C 2 -90 C 3 206 C 3 90 C 3 -244 C 2 -111 C 3 -74 C 3 -12 C 2 166 C 3 20 C 3 -28 C 2 0 C 3 -268 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f(in)g(Section)f(2,)g(as)g(determined)h(b)m(y)f(the)h(follo)m(wing)f (constan)m(ts:)811 501 y Fs(!)873 516 y Fo(0)945 501 y Fy(=)1062 433 y(1)p 1062 478 50 4 v 1062 569 a(8)1124 501 y Fs(m\032)1263 516 y Fq(I)1342 501 y Fs(;)215 b(c)1628 516 y Fo(0)1701 501 y Fy(=)28 b(11)1918 433 y Fs(M)p 1918 478 108 4 v 1928 569 a(m)2070 501 y(;)216 b(")2360 516 y Fo(0)2432 501 y Fy(=)29 b(2)2588 460 y Fg(\000)p Fo(10)2828 433 y Fs(m\032)2967 397 y Fo(2)2967 461 y Fq(I)p 2763 478 315 4 v 2763 569 a Fs(c)2806 535 y Fo(2)p Fq(n)2806 596 y Fo(0)2916 569 y Fr(j)p Fs(f)11 b Fr(j)3031 599 y Fq(\032)0 801 y Fy(\()p Fs(m)p Fy(,)33 b Fs(M)44 b Fy(are)33 b(de\014ned)i(in)f(\(2.5\))e(and)h(\(2.6\))f(resp)s(ectiv)m (ely\).)0 1015 y Fz(Lemma)38 b(1.)45 b Ft(Let)33 b Fs(")28 b Fr(\024)g Fs(")932 1030 y Fo(0)978 1015 y Ft(,)k(and)i(consider)i (any)d Fs(N)11 b Ft(-lattice)36 b Fy(\003)p Ft(.)44 b(Denote)651 1285 y Fs(\032)703 1244 y Fo(\003)703 1309 y Fq(I)790 1285 y Fy(=)28 b(8)974 1217 y Fs(\016)1018 1232 y Fo(\003)p 974 1262 104 4 v 982 1353 a Fs(m)1117 1285 y(<)g(\032)1274 1300 y Fq(I)1353 1285 y Fs(;)215 b(\032)1648 1244 y Fo(\003)1735 1285 y Fy(=)28 b(\()p Fs(\032)1931 1244 y Fo(\003)1931 1309 y Fq(I)1990 1285 y Fs(;)17 b(\032)2087 1300 y Fq(')2143 1285 y Fy(\))33 b Fs(;)215 b(\032)2510 1244 y Fo(\003)2510 1309 y Fg(\003)2597 1285 y Fy(=)28 b(\()2753 1246 y Fo(1)p 2753 1262 40 4 v 2753 1319 a(2)2805 1285 y Fs(\032)2857 1244 y Fo(\003)2857 1309 y Fq(I)2916 1285 y Fs(;)2988 1246 y Fo(1)p 2988 1262 V 2988 1319 a(6)3040 1285 y Fs(\032)3092 1300 y Fq(')3149 1285 y Fy(\))33 b Fs(:)0 1551 y Ft(There)h(exists)h(a) e(real)h(analytic)h(canonical)h(map)e Fy(\()p Fs(I)8 b(;)17 b(')p Fy(\))26 b(=)i Fr(C)2206 1566 y Fo(\003)2266 1551 y Fy(\()p Fs(I)2357 1514 y Fg(0)2384 1551 y Fs(;)17 b(')2494 1514 y Fg(0)2522 1551 y Fy(\))p Ft(,)32 b Fr(C)2673 1566 y Fo(\003)2761 1551 y Fy(:)27 b Fr(D)2896 1514 y Fo(\003)2893 1584 y Fq(\032)2934 1564 y Ff(\003)2934 1604 y Fc(\003)3018 1551 y Fr(!)g(D)3225 1514 y Fo(\003)3222 1584 y Fq(\032)3263 1564 y Ff(\003)3318 1551 y Ft(,)33 b(such)i(that:)15 1712 y(\(i\))83 b Fs(H)41 b Ft(is)35 b(conjugated)f(to)f Fs(H)1107 1727 y Fo(\003)1194 1712 y Fy(=)28 b Fs(H)i Fr(\016)22 b(C)1536 1727 y Fo(\003)1629 1712 y Ft(of)34 b(the)g(fo)m(rm)871 1951 y Fs(H)954 1966 y Fo(\003)1014 1951 y Fy(\()p Fs(I)1105 1910 y Fg(0)1132 1951 y Fs(;)17 b(')1242 1910 y Fg(0)1269 1951 y Fy(\))28 b(=)g Fs(h)p Fy(\()p Fs(I)1589 1910 y Fg(0)1617 1951 y Fy(\))22 b(+)g Fs("f)1872 1966 y Fo(\003)1932 1951 y Fy(\()p Fs(I)2023 1910 y Fg(0)2050 1951 y Fs(;)17 b(')2160 1910 y Fg(0)2188 1951 y Fy(\))k(+)i Fs("e)2440 1910 y Fg(\000)2515 1883 y Ff(1)p 2515 1894 34 4 v 2515 1934 a(6)2561 1910 y Fq(N)7 b(\032)2672 1920 y Fe(')2729 1951 y Fr(R)2813 1966 y Fo(\003)2873 1951 y Fy(\()p Fs(I)2964 1910 y Fg(0)2991 1951 y Fs(;)17 b(')3101 1910 y Fg(0)3128 1951 y Fy(\))33 b Fs(;)467 b Fy(\(4)p Fs(:)p Fy(2\))199 2174 y Ft(where)35 b Fs(f)524 2189 y Fo(\003)616 2174 y Ft(has)f(F)m(ourier)g(comp)s(onents)h(only)g(in)f Fy(\003)p Ft(,)f(i.e.)1387 2412 y Fs(f)1436 2427 y Fo(\003)1495 2412 y Fy(\()p Fs(I)1586 2371 y Fg(0)1614 2412 y Fs(;)17 b(')1724 2371 y Fg(0)1751 2412 y Fy(\))28 b(=)1927 2317 y Fh(X)1923 2532 y Fq(k)r Fg(2)p Fo(\003)2113 2386 y Fy(^)2092 2412 y Fs(f)2141 2427 y Fo(\003)p Fq(;k)2268 2412 y Fy(\()p Fs(I)2359 2371 y Fg(0)2386 2412 y Fy(\))p Fs(e)2471 2371 y Fq(ik)r Fg(\001)p Fq(')2619 2341 y Fc(0)2684 2412 y Fs(;)983 b Fy(\(4)p Fs(:)p Fy(3\))199 2730 y Ft(and)34 b Fs(f)432 2745 y Fo(\003)492 2730 y Ft(,)e Fr(R)636 2745 y Fo(\003)730 2730 y Ft(a)m(re)h(b)s(ounded)j(b)m(y)1406 2953 y Fr(j)p Fs(f)1483 2968 y Fo(\003)1542 2953 y Fr(j)1569 2903 y Fo(\003)1569 2983 y Fq(\032)1610 2963 y Ff(\003)1610 3003 y Fc(\003)1716 2953 y Fs(;)216 b Fr(j)o(R)2071 2968 y Fo(\003)2131 2953 y Fr(j)2159 2903 y Fo(\003)2159 2983 y Fq(\032)2200 2963 y Ff(\003)2200 3003 y Fc(\003)2283 2953 y Fr(\024)28 b Fy(2)17 b Fr(j)o Fs(f)11 b Fr(j)2570 2983 y Fq(\032)2666 2953 y Fs(:)1001 b Fy(\(4)p Fs(:)p Fy(4\))-9 3192 y Ft(\(ii\))84 b(The)34 b(transfo)m(rmation)h Fr(C)1088 3207 y Fo(\003)1182 3192 y Ft(is)f(nea)m(r)g(to)f(the)h (identit)m(y)i(fo)m(r)e(small)h Fs(")p Ft(,)e(and)h(in)h(pa)m(rticula)m (r)h(it)e(is)1669 3415 y Fr(k)p Fs(I)1771 3374 y Fg(0)1821 3415 y Fr(\000)22 b Fs(I)8 b Fr(k)28 b Fs(<)2187 3376 y Fo(1)p 2167 3392 80 4 v 2167 3449 a(64)2258 3415 y Fs(\032)2310 3374 y Fo(\003)2310 3440 y Fq(I)2402 3415 y Fs(:)-33 3638 y Ft(\(iii\))85 b(F)m(o)m(r)34 b(any)f(real)h(analytic) h Fs(u)28 b Fy(:)f Fr(D)1303 3602 y Fo(\003)1300 3666 y Fq(\032)1341 3646 y Fc(0)1401 3638 y Fr(!)h Fz(C)p Ft(,)k(with)j Fs(\032)1937 3602 y Fg(0)1992 3638 y Fy(=)28 b(\()p Fs(\032)2188 3602 y Fg(0)2188 3666 y Fq(I)2233 3638 y Fs(;)17 b(\032)2330 3602 y Fg(0)2330 3663 y Fq(')2386 3638 y Fy(\))33 b Ft(such)i(that)1157 3843 y Fo(1)p 1137 3859 V 1137 3916 a(16)1229 3882 y Fs(\032)1281 3841 y Fo(\003)1281 3906 y Fq(I)1367 3882 y Fr(\024)28 b Fs(\032)1524 3841 y Fg(0)1524 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v 2241 5281 a(2)p Fe(n)2347 5254 y(\032)2383 5264 y(')p 2347 5281 87 4 v 2374 5321 a Ff(6)1900 5579 y Fy(20)p eop %%Page: 21 21 21 20 bop 0 100 a Ft(it)34 b(is)g Fs(I)240 63 y Fg(0)268 100 y Fy(\()p Fs(t)p Fy(\))27 b Fr(2)h(B)571 63 y Fo(\003)568 133 y Fq(\032)609 113 y Ff(\003)609 153 y Fc(\003)665 100 y Ft(,)33 b(and)144 375 y Fr(k)p Fs(I)246 334 y Fg(0)274 375 y Fy(\()p Fs(t)p Fy(\))21 b Fr(\000)i Fs(I)561 334 y Fg(0)589 375 y Fy(\(0\))p Fr(k)j(\024)911 336 y Fo(1)p 911 352 40 4 v 911 409 a(3)979 375 y Fs(\032)1031 334 y Fo(\003)1031 400 y Fq(I)1123 375 y Fs(;)216 b Fr(k)p Fs(I)1469 334 y Fg(0)1496 375 y Fy(\()p Fs(t)p Fy(\))22 b Fr(\000)g Fs(I)8 b Fy(\(0\))p Fr(k)27 b(\024)2125 336 y Fo(7)p 2105 352 80 4 v 2105 409 a(20)2213 375 y Fs(\032)2265 334 y Fo(\003)2265 400 y Fq(I)2357 375 y Fs(;)215 b Fr(k)p Fs(I)8 b Fy(\()p Fs(t)p Fy(\))21 b Fr(\000)i Fs(I)8 b Fy(\(0\))p Fr(k)26 b(\024)3311 336 y Fo(1)p 3311 352 40 4 v 3311 409 a(2)3379 375 y Fs(\032)3431 334 y Fo(\003)3431 400 y 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Fq(k)2212 5340 y Fy(\()p Fs(t)p Fy(\))33 b Fs(;)1308 b Fy(\(4)p Fs(:)p Fy(8\))1900 5579 y(21)p eop %%Page: 22 22 22 21 bop 0 100 a Fy(where)1002 219 y Fs(g)1054 171 y Fq(\034)t(;)p Fo(0)1050 249 y Fq(k)1162 219 y Fy(\()p Fs(t)p Fy(\))28 b(=)g Fr(F)1481 234 y Fq(k)1529 219 y Fy(\()1579 194 y(~)1568 219 y(\010)1640 177 y Fq(t)p Fg(\000)p Fq(\034)1640 248 y Fo(\003)1782 219 y Fy(\(\010)1893 178 y Fq(\034)1893 244 y Fo(\003)1952 219 y Fy(\()p Fs(I)2043 178 y Fg(0)2071 219 y Fy(\(0\))p Fs(;)17 b(')2309 178 y Fg(0)2335 219 y Fy(\(0\)\)\))p Fs(e)2587 178 y Fg(\000)p Fq(ik)r Fg(\001)p Fo(\012)p Fq(t)2870 219 y Fs(;)0 415 y Fy(and)31 b Fs(g)243 367 y Fq(\034)t(;)p Fo(1)239 445 y Fq(k)351 415 y Fy(\()p Fs(t)p Fy(\))g(is)g(de\014ned)h(b)m(y)g (di\013erence;)1554 390 y(~)1543 415 y(\010)1615 379 y Fq(t)1615 443 y Fo(\003)1705 415 y Fy(denotes)g(the)f(\015o)m(w)g(of) 2575 390 y(~)2549 415 y Fs(H)2632 430 y Fo(\003)2691 415 y Fy(.)43 b(It)31 b(is)g(w)m(orth)m(while)g(to)f(remark)0 548 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