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cleartomark
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%%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
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dup 44 /comma put
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dup 54 /six put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
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readonly def
/FontBBox{-163 -250 1146 969}readonly def
/UniqueID 5000828 def
currentdict end
currentfile eexec
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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 /minus put
readonly def
/FontBBox{-4 -948 1329 786}readonly def
/UniqueID 5000816 def
currentdict end
currentfile eexec
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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 78 /N put
dup 82 /R 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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cleartomark
%%EndFont 
%%BeginFont: MSAM10
%!PS-AdobeFont-1.1: MSAM10 2.1
%%CreationDate: 1993 Sep 17 09:05:00
% 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 (MSAM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSAM10 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 3 /square put
readonly def
/FontBBox{8 -463 1331 1003}readonly def
/UniqueID 5031981 def
currentdict end
currentfile eexec
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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 2 /bracketleftbig put
dup 3 /bracketrightbig put
dup 8 /braceleftbig put
dup 9 /bracerightbig put
dup 18 /parenleftbigg put
dup 19 /parenrightbigg put
dup 34 /bracketleftBigg put
dup 35 /bracketrightBigg put
dup 40 /braceleftBigg put
dup 48 /parenlefttp put
dup 49 /parenrighttp put
dup 64 /parenleftbt put
dup 65 /parenrightbt put
dup 66 /parenleftex put
dup 67 /parenrightex put
dup 80 /summationtext put
dup 84 /intersectiontext put
dup 90 /integraldisplay put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueID 5000774 def
currentdict end
currentfile eexec
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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 11 /alpha put
dup 12 /beta put
dup 27 /sigma put
dup 96 /lscript put
dup 105 /i put
dup 107 /k put
dup 114 /r put
dup 115 /s put
readonly def
/FontBBox{11 -250 1241 750}readonly def
/UniqueID 5087381 def
currentdict end
currentfile eexec
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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 78 /N put
dup 82 /R put
readonly def
/FontBBox{-55 -420 2343 920}readonly def
/UniqueID 5031982 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMTI12
%!PS-AdobeFont-1.1: CMTI12 1.0
%%CreationDate: 1991 Aug 18 21:06:53
% 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 (CMTI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI12 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 11 /ff put
dup 12 /fi put
dup 14 /ffi put
dup 34 /quotedblright put
dup 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 49 /one put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 58 /colon put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 76 /L put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 87 /W put
dup 92 /quotedblleft put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
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dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
readonly def
/FontBBox{-36 -251 1103 750}readonly def
/UniqueID 5000829 def
currentdict end
currentfile eexec
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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 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 73 /I put
dup 76 /L put
dup 82 /R put
dup 97 /a put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 105 /i put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 118 /v put
readonly def
/FontBBox{-39 -250 1036 750}readonly def
/UniqueID 5000792 def
currentdict end
currentfile eexec
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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 /minus put
dup 1 /periodcentered put
dup 2 /multiply put
dup 10 /circlemultiply put
dup 24 /similar put
dup 33 /arrowright put
dup 49 /infinity put
dup 50 /element put
dup 54 /negationslash put
dup 102 /braceleft put
dup 103 /braceright put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
/UniqueID 5000818 def
currentdict end
currentfile eexec
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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 43 /plus put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
readonly def
/FontBBox{-20 -250 1193 750}readonly def
/UniqueID 5000789 def
currentdict end
currentfile eexec
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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 11 /alpha put
dup 14 /delta put
dup 17 /eta put
dup 21 /lambda put
dup 26 /rho put
dup 27 /sigma put
dup 33 /omega put
dup 34 /epsilon put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 69 /E put
dup 73 /I put
dup 78 /N put
dup 85 /U put
dup 88 /X put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 110 /n put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 120 /x put
dup 121 /y put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueID 5087383 def
currentdict end
currentfile eexec
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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 8 /Phi put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 53 /five put
dup 59 /semicolon put
dup 61 /equal put
dup 103 /g put
dup 108 /l put
dup 111 /o put
dup 126 /tilde put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 def
currentdict end
currentfile eexec
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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 /minus put
dup 1 /periodcentered put
dup 2 /multiply put
dup 8 /circleplus put
dup 14 /openbullet put
dup 17 /equivalence put
dup 20 /lessequal put
dup 21 /greaterequal put
dup 26 /propersubset put
dup 33 /arrowright put
dup 49 /infinity put
dup 50 /element put
dup 54 /negationslash put
dup 77 /M put
dup 82 /R put
dup 84 /T put
dup 87 /W put
dup 91 /union put
dup 102 /braceleft put
dup 103 /braceright put
dup 106 /bar put
dup 107 /bardbl put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueID 5000820 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI12
%!PS-AdobeFont-1.1: CMMI12 1.100
%%CreationDate: 1996 Jul 27 08:57:55
% 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 (CMMI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI12 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 11 /alpha put
dup 12 /beta put
dup 13 /gamma put
dup 14 /delta put
dup 17 /eta put
dup 21 /lambda put
dup 27 /sigma put
dup 31 /chi put
dup 33 /omega put
dup 34 /epsilon put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 72 /H put
dup 73 /I put
dup 78 /N put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 85 /U put
dup 88 /X put
dup 89 /Y put
dup 96 /lscript put
dup 100 /d put
dup 101 /e put
dup 105 /i put
dup 107 /k put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-30 -250 1026 750}readonly def
/UniqueID 5087386 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMCSC10
%!PS-AdobeFont-1.1: CMCSC10 1.0
%%CreationDate: 1991 Aug 18 17:46:49
% 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 (CMCSC10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMCSC10 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 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 55 /seven put
dup 56 /eight put
dup 65 /A put
dup 73 /I put
dup 78 /N put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 88 /X put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
readonly def
/FontBBox{14 -250 1077 750}readonly def
/UniqueID 5000772 def
currentdict end
currentfile eexec
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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 /Gamma put
dup 5 /Pi put
dup 8 /Phi put
dup 9 /Psi put
dup 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 14 /ffi put
dup 19 /acute put
dup 22 /macron put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 61 /equal put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 90 /Z put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 95 /dotaccent put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
dup 126 /tilde put
dup 127 /dieresis put
readonly def
/FontBBox{-34 -251 988 750}readonly def
/UniqueID 5000794 def
currentdict end
currentfile eexec
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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 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 19 /acute put
dup 35 /numbersign put
dup 38 /ampersand put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueID 5000793 def
currentdict end
currentfile eexec
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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 13 /fl put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
readonly def
/FontBBox{-53 -251 1139 750}readonly def
/UniqueID 5000769 def
currentdict end
currentfile eexec
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TeXDict begin 40258431 52099146 1000 600 600 (paper.dvi)
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2[44 32[44 17[44 46[{}13 83.022 /CMTT10 rf /Fb 134[40
2[38 45 28 34 35 38 42 42 47 68 21 38 1[25 42 38 25 38
42 38 38 42 6[51 1[62 1[62 62 59 47 2[56 64 62 74 52
1[44 32 62 64 1[56 63 59 58 62 6[25 42 42 1[42 4[42 2[25
30 25 2[34 34 28[51 11[{}53 83.022 /CMTI10 rf /Fc 255[48{}1
49.8132 /CMSY6 rf /Fd 165[44 7[48 3[48 78[{}3 66.4176
/MSBM7 rf /Fe 252[77 3[{}1 99.6264 /MSAM10 rf /Ff 165[55
5[83 3[105 12[87 87 87 87 14[87 87 7[80 4[58 58 14[73
73 8[58 58 4[42 42 46 46{}20 99.6264 /CMEX10 rf /Fg 140[29
29 6[33 1[22 8[26 68[36 14[35 40 11[{}8 49.8132 /CMMI6
rf /Fh 173[72 3[72 78[{}2 99.6264 /MSBM10 rf /Fi 132[50
40 47 45 65 45 52 32 40 41 1[50 50 55 80 25 45 30 30
50 45 30 45 50 45 45 50 4[50 4[97 2[70 55 71 1[66 75
72 1[61 1[51 38 72 75 64 1[74 70 69 72 6[30 3[50 50 50
50 1[50 2[30 35 30 2[40 40 5[50 19[86 1[55 60 11[{}59
99.6264 /CMTI12 rf /Fj 137[41 1[30 30 30 2[38 43 64 21
2[21 2[23 34 43 2[38 14[57 5[48 2[28 15[38 38 38 38 38
38 38 38 38 38 1[21 46[{}27 74.7198 /CMR9 rf /Fk 152[35
35 47[0 3[47 71 15[71 8[55 13[55 7[55 20 55{}11 66.4176
/CMSY8 rf /Fl 205[30 30 30 4[47 43[{}4 49.8132 /CMR6
rf /Fm 134[35 40 3[25 33 32 3[43 2[37 29 24 4[36 31 30
37 8[58 2[48 6[56 4[31 3[52 1[50 53 53 2[55 35 55 20
20 23[33 44 5[40 36 4[41 3[35 2[31 2[45 11[{}34 66.4176
/CMMI8 rf /Fn 129[35 14[35 2[20 4[35 41[55 1[20 5[35
1[35 35 35 35 4[55 1[27 27 31[51 8[{}15 66.4176 /CMR8
rf /Fo 148[50 28 2[50 50 10[66 3[98 2[54 1[84 4[120 22[0
3[66 100 15[100 6[77 4[77 77 2[77 2[50 5[77 5[77 28 77{}22
99.6264 /CMSY10 rf /Fp 133[45 48 55 2[56 35 46 44 6[51
1[33 3[45 51 3[41 6[57 81 2[66 1[60 74 1[63 1[78 4[43
81 1[63 72 81 70 74 73 2[76 49 76 27 27 23[46 61 1[61
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rf /Fq 135[61 83 1[61 59 46 60 1[56 63 61 74 51 63 1[30
61 64 53 56 62 59 1[61 12[78 61 80 1[74 1[81 4[40 7[81
13[55 1[55 2[32 46[{}30 99.6264 /CMCSC10 rf /Fr 128[49
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51 30 27 54 49 30 43 54 43 54 49 1[27 1[27 1[27 60 2[100
73 73 70 54 72 1[66 76 73 89 61 76 50 35 73 77 64 66
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1[27 33 27 76 1[38 38 27 16[49 2[49 4[81 54 54 57 1[76
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49 38 50 2[53 51 4[25 2[44 46 1[49 48 51 8[68 2[68 65
51 17[68 8[46 46 4[46 46 46 1[27 31 27 44[{}27 83.022
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46 42 46 69 23 44 1[23 46 42 25 37 46 37 46 42 3[23 1[23
51 62 62 85 62 1[60 46 61 1[57 65 62 76 52 65 43 30 62
65 54 57 63 60 59 62 6[23 42 42 42 42 42 42 42 42 42
42 1[23 28 23 2[32 32 23 65 2[69 15[42 5[46 46 48 11[{}75
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62 93 31 59 1[31 62 56 34 51 62 50 62 54 9[116 85 86
78 62 84 1[77 84 88 106 67 2[42 88 88 70 74 86 81 80
85 6[31 56 56 56 56 56 56 56 56 56 56 1[31 37 31[62 13[{}57
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%%Page: 15 15
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%%Page: 16 16
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%%Page: 24 24
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y(cannot)33 b(assume)h(that)f(\000)1386 2823 y Fn(\010)1386
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b(functions)i(\010)f(ha)m(v)m(e)g(domain)g(in)f(all)h(of)f
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3091 y Fr(\).)43 b(This)34 b(is)f(done)g(in)g(Section)g(4.1.)555
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3171 y Fm(sA)1879 3180 y Fl(2)1949 3207 y Fr(is)h(a)e(con)m(traction)i
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g(in)g Fp(C)3126 3287 y Fn(0)3195 3324 y Fr(norm.)456
3440 y(Also,)h(using)h(the)g(same)g(form)m(ulas)f(for)g(the)g(high)g
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3556 y(sho)m(w)g(that)g(the)g Fp(\037)f Fr(spaces)i(get)f(mapp)s(ed)g
(in)m(to)g(themselv)m(es.)1393 3780 y(7.)48 b Fq(A)m(ckno)n
(wledgements)555 3954 y Fr(The)38 b(w)m(ork)f(of)f(the)h(author)f(has)h
(b)s(een)g(supp)s(orted)g(b)m(y)h(NSF)e(gran)m(ts)h(and)f(b)m(y)456
4070 y(a)46 b(Dean's)h(fello)m(wship)i(at)d(Univ.)87
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(in)f(the)h(W)-8 b(orking)43 b(Dynamical)456 4303 y(Systems)j(Seminar,)
i(U.T)-8 b(exas)46 b(F)-8 b(all)44 b(2002,)i(made)f(v)m(ery)h(v)-5
b(aluable)44 b(commen)m(ts)456 4419 y(ab)s(out)32 b(the)i(presen)m
(tation)g(of)f(this)g(material.)45 b(Thanks)35 b(also)e(to)g(E.)g(F)-8
b(on)m(tic)m(h)34 b(for)456 4535 y(v)m(ery)g(enligh)m(tening)g
(discussions)h(and)e(a)f(careful)h(reading)g(of)f(the)h(pap)s(er.)1660
4759 y Fq(References)456 4917 y Ft([CFdlL03a])45 b(Xa)n(vier)34
b(Cabr)n(\023)-39 b(e,)37 b(Ernest)e(F)-7 b(on)n(tic)n(h,)38
b(and)e(Rafael)f(de)h(la)g(Lla)n(v)n(e.)f(The)h(parame-)908
5016 y(terization)h(metho)r(d)h(for)g(in)n(v)-5 b(arian)n(t)36
b(manifolds)i(I:)g(manifolds)g(asso)r(ciated)f(to)908
5116 y(non-resonan)n(t)30 b(subspaces.)h Fb(Ind.)j(Univ.)h(Math.)g
(Jour)p Ft(,)e(52\(2\):283{328,)c(2003.)908 5216 y(MP)p
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b(and)e(Rafael)f(de)h(la)g(Lla)n(v)n(e.)f(The)h(parame-)908
550 y(terization)f(metho)r(d)i(for)f(in)n(v)-5 b(arian)n(t)36
b(manifolds)g(I)r(I:)h(regularit)n(y)e(with)i(resp)r(ect)908
649 y(to)28 b(parameters.)f Fb(Ind.)k(Univ.)g(Math.)g(Jour)p
Ft(,)e(52\(2\):329{360,)24 b(2003.)j(MP)p 3239 649 25
4 v 29 w(AR)n(C)908 749 y(#02-511.)456 849 y([CFdlL03c])50
b(Xa)n(vier)25 b(Cabr)n(\023)-39 b(e,)24 b(Ernest)i(F)-7
b(on)n(tic)n(h,)26 b(and)g(Rafael)g(de)g(la)g(Lla)n(v)n(e.)f(The)h
(parameter-)908 948 y(ization)i(metho)r(d)h(for)g(in)n(v)-5
b(arian)n(t)27 b(manifolds)i(III:)g(o)n(v)n(erview)e(and)h
(applications.)908 1048 y Fb(In)h(pr)l(ep)l(ar)l(ation)p
Ft(,)g(2003.)456 1147 y([DGZ93])143 b(Rob)r(ert)36 b(Deville,)k(Gilles)
d(Go)r(defro)n(y)-7 b(,)38 b(and)f(V\023)-42 b(acla)n(v)35
b(Zizler.)i Fb(Smo)l(othness)h(and)908 1247 y(r)l(enormings)d(in)f
(Banach)j(sp)l(ac)l(es)p Ft(,)e(v)n(olume)d(64)g(of)h
Fb(Pitman)i(Mono)l(gr)l(aphs)i(and)908 1347 y(Surveys)24
b(in)g(Pur)l(e)g(and)h(Applie)l(d)g(Mathematics)p Ft(.)f(Longman)c
(Scien)n(ti\014c)i(&)f(T)-7 b(ec)n(h-)908 1446 y(nical,)27
b(Harlo)n(w,)f(1993.)456 1546 y([dlL97])201 b(Rafael)22
b(de)g(la)g(Lla)n(v)n(e.)f(In)n(v)-5 b(arian)n(t)21 b(manifolds)i(asso)
r(ciated)e(to)h(nonresonan)n(t)f(sp)r(ec-)908 1646 y(tral)27
b(subspaces.)f Fb(J.)k(Statist.)f(Phys.)p Ft(,)h(87\(1-2\):211{249,)22
b(1997.)456 1745 y([dlL)-9 b(W95])125 b(Rafael)40 b(de)h(la)f(Lla)n(v)n
(e)f(and)i(C.)g(Eugene)e(W)-7 b(a)n(yne.)41 b(On)f(Irwin's)g(pro)r(of)g
(of)h(the)908 1845 y(pseudostable)26 b(manifold)i(theorem.)f
Fb(Math.)k(Z.)p Ft(,)d(219\(2\):301{321,)23 b(1995.)456
1944 y([Hal80])195 b(Jac)n(k)25 b(K.)i(Hale.)g Fb(Or)l(dinary)j
(di\013er)l(ential)h(e)l(quations)p Ft(.)c(Rob)r(ert)g(E.)g(Krieger)e
(Pub-)908 2044 y(lishing)i(Co.)g(Inc.,)h(Hun)n(tington,)g(N.Y.,)g
(second)f(edition,)h(1980.)456 2144 y([HP70])203 b(Morris)29
b(W.)j(Hirsc)n(h)f(and)g(Charles)f(C.)i(Pugh.)f(Stable)g(manifolds)g
(and)g(h)n(yp)r(er-)908 2243 y(b)r(olic)i(sets.)h(In)g
Fb(Glob)l(al)j(A)n(nalysis)f(\(Pr)l(o)l(c.)g(Symp)l(os.)g(Pur)l(e)f
(Math.,)k(V)-6 b(ol.)36 b(XIV,)908 2343 y(Berkeley,)29
b(Calif.,)h(1968\))p Ft(,)d(pages)c(133{163.)e(Amer.)k(Math.)f(So)r
(c.,)h(Pro)n(vidence,)908 2443 y(R.I.,)j(1970.)456 2542
y([HPS77])157 b(M.W.)24 b(Hirsc)n(h,)g(C.C.)f(Pugh,)h(and)g(M.)g(Sh)n
(ub.)g Fb(Invariant)i(manifolds)p Ft(.)g(Springer-)908
2642 y(V)-7 b(erlag,)26 b(Berlin,)h(1977.)f(Lecture)h(Notes)h(in)g
(Mathematics,)f(V)-7 b(ol.)28 b(583.)456 2742 y([Irw80])199
b(M.C.)40 b(Irwin.)f(A)h(new)g(pro)r(of)f(of)g(the)i(pseudostable)d
(manifold)i(theorem.)f Fb(J.)908 2841 y(L)l(ondon)30
b(Math.)h(So)l(c.)p Ft(,)d(21:557{566,)c(1980.)456 2941
y([JPdlL95])101 b(M.)37 b(Jiang,)h(Y)-7 b(a.)37 b(B.)g(P)n(esin,)i(and)
e(R.)g(de)g(la)g(Lla)n(v)n(e.)e(On)i(the)h(in)n(tegrabilit)n(y)e(of)908
3040 y(in)n(termediate)19 b(distributions)h(for)g(Anoso)n(v)f
(di\013eomorphisms.)g Fb(Er)l(go)l(dic)25 b(The)l(ory)908
3140 y(Dynam.)30 b(Systems)p Ft(,)d(15\(2\):317{331,)d(1995.)456
3240 y([Kat95])183 b(T)-7 b(osio)23 b(Kato.)g Fb(Perturb)l(ation)k(the)
l(ory)g(for)h(line)l(ar)f(op)l(er)l(ators)p Ft(.)e(Classics)e(in)i
(Math-)908 3339 y(ematics.)i(Springer-V)-7 b(erlag,)25
b(Berlin,)i(1995.)f(Reprin)n(t)i(of)f(the)h(1980)e(edition.)456
3439 y([LI73])240 b(Oscar)32 b(E.)h(Lanford)g(III.)h(Bifurcation)f(of)h
(p)r(erio)r(dic)g(solutions)f(in)n(to)h(in)n(v)-5 b(arian)n(t)908
3539 y(tori:)32 b(the)19 b(w)n(ork)e(of)i(Ruelle)g(and)g(T)-7
b(ak)n(ens.)18 b(In)h(Iv)-5 b(ar)18 b(Stakgold,)i(Daniel)f(D.)g
(Joseph,)908 3638 y(and)35 b(Da)n(vid)h(H.)g(Sattinger,)h(editors,)g
Fb(Nonline)l(ar)g(pr)l(oblems)i(in)e(the)g(Physic)l(al)908
3738 y(Scienc)l(es)24 b(and)g(biolo)l(gy:)38 b(Pr)l(o)l(c)l(e)l(e)l
(dings)25 b(of)f(a)h(Battel)t(le)g(summer)e(institute)p
Ft(,)f(pages)908 3837 y(159{192,)e(Berlin,)k(1973.)d(Springer-V)-7
b(erlag.)21 b(Lecture)h(Notes)h(in)h(Mathematics,)908
3937 y(V)-7 b(ol.)27 b(322.)456 4037 y([LI83])240 b(Oscar)27
b(E.)j(Lanford)e(III.)i(In)n(tro)r(duction)f(to)g(the)h(mathematical)g
(theory)e(of)i(dy-)908 4136 y(namical)40 b(systems.)g(In)g
Fb(Chaotic)k(b)l(ehavior)g(of)e(deterministic)h(systems)e(\(L)l(es)908
4236 y(Houches,)30 b(1981\))p Ft(,)g(pages)c(3{51.)g(North-Holland,)h
(Amsterdam,)g(1983.)456 4336 y([Rue89])178 b(Da)n(vid)25
b(Ruelle.)h Fb(Elements)h(of)i(di\013er)l(entiable)g(dynamics)g(and)g
(bifur)l(c)l(ation)f(the-)908 4435 y(ory)p Ft(.)g(Academic)g(Press)e
(Inc.,)i(Boston,)e(MA,)i(1989.)456 4535 y([Sho97])188
b(R.)32 b(E.)g(Sho)n(w)n(alter.)f Fb(Monotone)k(op)l(er)l(ators)g(in)f
(Banach)i(sp)l(ac)l(e)e(and)h(nonline)l(ar)908 4634 y(p)l(artial)h
(di\013er)l(ential)h(e)l(quations)p Ft(.)d(American)g(Mathematical)f
(So)r(ciet)n(y)-7 b(,)36 b(Pro)n(vi-)908 4734 y(dence,)27
b(RI,)h(1997.)456 4834 y([Sh)n(u87])186 b(Mic)n(hael)30
b(Sh)n(ub.)i Fb(Glob)l(al)j(stability)f(of)g(dynamic)l(al)h(systems)p
Ft(.)c(Springer-V)-7 b(erlag,)908 4933 y(New)39 b(Y)-7
b(ork,)43 b(1987.)37 b(With)k(the)f(collab)r(oration)e(of)h(Alb)r(ert)i
(F)-7 b(athi)40 b(and)f(R)n(\023)-39 b(emi)908 5033 y(Langevin,)26
b(T)-7 b(ranslated)27 b(from)g(the)h(F)-7 b(renc)n(h)27
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