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% 
% Authors: S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry, W. Schmidt
%
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% 0x80
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% 0x90
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% 0xA0
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% 0xD0
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% 0xF0
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% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
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/FontInfo 7 dict dup begin
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/Weight (Medium) readonly def
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readonly def
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%%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
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readonly def
/FontBBox{-301 -250 1164 946}readonly def
/UniqueID 5000768 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSL10
%!PS-AdobeFont-1.1: CMSL10 1.0
%%CreationDate: 1991 Aug 20 16:40:20
% 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 (CMSL10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -9.46 def
/isFixedPitch false def
end readonly def
/FontName /CMSL10 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{-62 -250 1123 750}readonly def
/UniqueID 5000798 def
currentdict end
currentfile eexec
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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
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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 0 /.notdef put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueID 5000793 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%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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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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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 0 /.notdef put
readonly def
/FontBBox{-30 -250 1026 750}readonly def
/UniqueID 5087386 def
currentdict end
currentfile eexec
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%%EndFont 
%%BeginFont: CMSS12
%!PS-AdobeFont-1.1: CMSS12 1.0
%%CreationDate: 1991 Aug 20 17:33:47
% 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 (CMSS12) readonly def
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/FontName /CMSS12 def
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/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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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
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readonly def
/FontBBox{8 -463 1331 1003}readonly def
/UniqueID 5031981 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMSL12
%!PS-AdobeFont-1.1: CMSL12 1.0
%%CreationDate: 1991 Aug 20 16:40:41
% 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 (CMSL12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -9.46 def
/isFixedPitch false def
end readonly def
/FontName /CMSL12 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{-56 -251 1102 750}readonly def
/UniqueID 5000799 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
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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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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 88 /summationdisplay put
dup 112 /radicalbig put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueID 5000774 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 0 /.notdef put
readonly def
/FontBBox{-53 -251 1139 750}readonly def
/UniqueID 5000769 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
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/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
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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 0 /.notdef put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 def
currentdict end
currentfile eexec
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%%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
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/FamilyName (Computer Modern) readonly def
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/FontName /CMTI12 def
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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 0 /.notdef put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueID 5087383 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
dup 84 /T put
dup 89 /Y 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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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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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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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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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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cleartomark
%%EndFont 
TeXDict begin 39158280 55380996 1000 600 600 (HH2008-3.dvi)
@start /Fa 146[62 1[53 9[51 97[{ TeX0ef0afcaEncoding ReEncodeFont }3
83.022 /CMCSC10 rf /Fb 198[48 48 48 48 48 48 48 48 48
48 48[{ TeXf7b6d320Encoding ReEncodeFont }10 83.022 /CMBX10
rf /Fc 128[42 4[37 44 1[60 44 46 32 33 33 1[46 42 46
69 23 44 1[23 46 42 1[37 46 37 46 42 7[62 62 85 62 1[60
46 61 65 57 65 62 76 52 65 43 30 62 65 54 2[60 59 62
5[23 23 11[23 28 23 4[23 13[42 25[{ TeXf7b6d320Encoding ReEncodeFont }
52 83.022 /CMSL10 rf /Fd 142[37 42 52[23 23 58[{
  TeXaae443f0Encoding ReEncodeFont }4 83.022 /CMMI10 rf
/Fe 132[42 1[44 44 60 44 46 32 33 33 44 46 42 46 69 23
44 25 23 46 42 25 37 46 37 46 42 23 2[23 42 23 2[62 85
62 62 60 46 61 65 57 1[62 76 52 65 1[30 62 65 54 1[63
60 59 62 1[39 3[23 23 42 42 42 42 42 42 42 42 42 42 1[23
28 23 2[32 32 23 3[69 42 21[46 48 11[{
  TeXf7b6d320Encoding ReEncodeFont }74 83.022 /CMR10 rf
/Ff 203[33 1[33 33 49[{ TeXf7b6d320Encoding ReEncodeFont }3
58.1154 /CMR7 rf /Fg 200[30 2[30 30 30 30 49[{
  TeXf7b6d320Encoding ReEncodeFont }5 49.8132 /CMR6 rf
/Fh 193[109 1[109 60[{ TeXaae443f0Encoding ReEncodeFont }2
143.462 /CMMI12 rf /Fi 172[54 83[{ TeXf7b6d320Encoding ReEncodeFont }1
99.6264 /CMSS12 rf /Fj 139[35 36 3[45 51 10[40 99[{
  TeXf7b6d320Encoding ReEncodeFont }5 90.9091 /CMSL10
rf /Fk 252[77 3[{}1 99.6264 /MSAM10 rf /Fl 131[98 2[51
1[70 51 54 38 38 38 51 54 49 54 81 27 2[27 54 49 30 43
54 43 54 49 9[100 2[70 7[61 2[35 7[73 18[27 33 27 29[81
14[{ TeXf7b6d320Encoding ReEncodeFont }32 99.6264 /CMSL12
rf /Fm 252[32 3[{ TeXbbad153fEncoding ReEncodeFont }1
49.8132 /CMSY6 rf /Fn 143[100 23[144 75[33 10[46 46{}5
99.6264 /CMEX10 rf /Fo 135[59 2[62 44 44 46 59 62 56
62 93 31 59 1[31 62 56 34 51 62 50 62 54 11[86 78 1[84
12[74 3[85 13[56 56 56 2[31 37 3[44 44 40[{
  TeXf7b6d320Encoding ReEncodeFont }33 99.6264 /CMBX12
rf /Fp 149[20 102[35 2[55{ TeXbbad153fEncoding ReEncodeFont }3
66.4176 /CMSY8 rf /Fq 129[35 31[35 32[55 4[35 1[35 35
35 35 35 35 35 4[55 9[20 33[{ TeXf7b6d320Encoding ReEncodeFont }13
66.4176 /CMR8 rf /Fr 139[32 40 41 2[50 55 80 25 2[30
50 45 30 45 50 2[50 12[70 3[66 12[70 16[50 50 2[30 46[{
  TeX74afc74cEncoding ReEncodeFont }20 99.6264 /CMTI12
rf /Fs 134[35 10[43 1[21 37 29 24 4[36 1[30 37 29 17[56
43[33 5[31 5[42 22[{ TeXaae443f0Encoding ReEncodeFont }14
66.4176 /CMMI8 rf /Ft 165[66 72 4[66 1[72 3[72 78[{}5
99.6264 /MSBM10 rf /Fu 143[83 1[50 3[28 39 39 50 50 22[79
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77 77 1[77 14[77 1[77{ TeXbbad153fEncoding ReEncodeFont }25
99.6264 /CMSY10 rf /Fv 134[48 55 6[43 49 1[58 1[29 51
40 5[51 42 41 51 41 9[57 66 6[78 4[43 81 2[72 81 70 74
73 51 1[76 1[76 27 27 18[64 4[46 61 4[42 4[48 59 57 3[48
3[51 55 62 11[{ TeXaae443f0Encoding ReEncodeFont }39
99.6264 /CMMI12 rf /Fw 128[81 6[85 1[85 90 63 64 66 1[90
81 90 134 45 2[45 1[81 49 74 90 72 90 78 14[120 6[126
1[60 126 4[117 1[122 11[81 81 81 81 81 49[{
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rf /Fx 152[42 1[42 54[28 46[{ TeX74afc74cEncoding ReEncodeFont }3
90.9091 /CMTI10 rf /Fy 255[71{ TeXbbad153fEncoding ReEncodeFont }1
90.9091 /CMSY10 rf /Fz 177[73 78[{ TeXaae443f0Encoding ReEncodeFont }1
90.9091 /CMMI10 rf /FA 128[45 5[48 48 66 48 51 35 36
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4761 y Fn(p)p 1642 4761 192 4 v 1642 4846 a Fv(\025)p
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4139 y Fu(\002)23 b Ft(T)35 b FD(and)f Fv(I)k FD(=)31
b(\()p Fv(y)t(;)17 b(p)p FD(\))33 b(with)109 4259 y(v)-5
b(alues)42 b(in)f Ft(R)602 4223 y Fs(n)677 4259 y Fu(\002)29
b Ft(R)p FD(,)43 b(where)f Fv(y)j FD(parametrises)d(the)g(surface)g
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4380 y(single)33 b(resonance)h(reads)1287 4477 y Fv(@)p
1263 4521 106 4 v 1263 4612 a(@)5 b(p)1378 4544 y(H)1459
4559 y Fq(0)1499 4544 y FD(\()p Fv(y)t(;)17 b FD(0\))81
b(=)i(0)130 b(for)32 b(all)g Fv(y)f Fu(2)d Ft(Y)49 b
Fv(;)1020 b FD(\(7\))109 4769 y(cf.)36 b([13,)h(14)o(,)g(24)o(,)g(10)o
(].)56 b(The)37 b(remaining)g(frequencies)i(form)e(the)f(v)m(ector)i
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4784 y Fq(0)3284 4769 y FD(\()p Fv(y)t(;)17 b FD(0\))35
b(whic)m(h)j(is)109 4889 y(non-resonan)m(t)c(at)f(a)g(single)i
(resonance)g(\()p Fv(y)t(;)17 b(p)p FD(\))28 b(=)h(\()p
Fv(y)2058 4853 y Fp(\003)2097 4889 y Fv(;)17 b FD(0\).)46
b(T)-8 b(reating)34 b Fv(!)j FD(as)c(an)h(external)h(parameter,)109
5010 y(w)m(e)c(exp)s(ect)g(p)s(ersistence)i(results)e(only)g(for)e
(Diophan)m(tine)i Fv(!)t FD(,)f(where)h(gaps)g(in)f(the)h(resulting)g
(`Can)m(tor)109 5130 y(set')k(corresp)s(ond)g(to)g(m)m(ultiple)h
(resonances.)51 b(F)-8 b(ollo)m(wing)69 b([22)o(,)35
b(9],)g(w)m(e)g(lo)s(calise)h(to)k(^)-55 b Fv(y)37 b
FD(\()p Fv(")p FD({close)e(to)f(0\))109 5250 y(writing)40
b Fv(y)k FD(=)c Fv(y)712 5214 y Fp(\003)778 5250 y FD(+)33
b(^)-55 b Fv(y)s FD(,)42 b(thereb)m(y)g(shrinking)f(the)g(neigh)m(b)s
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%%Page: 6 6
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417 y Fp(\003)1616 458 y Fv(;)g(!)t FD(\))82 b(=)h Fu(h)p
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Fv(y)1498 888 y Fp(\003)1537 929 y FD(\))83 b Fu(6)p
FD(=)f(0)130 b(for)32 b(all)h Fv(y)2332 888 y Fp(\003)2398
929 y Fu(2)28 b Ft(Y)49 b Fv(;)109 1149 y FD(whence)42
b(w)m(e)f(\014nd)g(a)f(lo)m(w)m(er)i(b)s(ound)e(of)g(the)h(function)g
Fu(j)p Fv(a)p Fu(j)f FD(b)m(y)h(shrinking)h(the)f(co-ordinate)f(domain)
109 1270 y Fv(U)e Fu(\033)28 b Ft(Y)33 b FD(a)f(bit)h(if)f(necessary)-8
b(.)109 1440 y(W)g(e)34 b(no)m(w)h(apply)g(a)f(familiar)g(metho)s(d)h
(to)f(replace)h(the)g(system)h(\(3\))e(b)m(y)h(a)f(family)h(of)f
(one-degree-of-)109 1560 y(freedom)i(systems,)k(cf.)c([2,)g(13,)g(24)o
(,)h(10)o(].)54 b(Starting)36 b(p)s(oin)m(t)g(is)h(a)f(normalizing)g
(transformation)g(that)109 1681 y(turns)d(the)g(p)s(erturb)s(ed)g
(Hamiltonian)g(in)m(to)546 1901 y Fv(H)627 1916 y Fs(")663
1901 y FD(\()p Fv(x;)24 b FD(^)-56 b Fv(y)s(;)17 b(p;)g(q)t
FD(;)g Fv(y)1131 1860 y Fp(\003)1169 1901 y Fv(;)g(!)t
FD(\))82 b(=)h Fv(H)1638 1916 y Fq(0)1677 1901 y FD(\()7
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1901 y Fv(H)2441 1916 y Fq(1)2480 1901 y FD(\()7 b(^)-56
b Fv(y)s(;)17 b(p;)g(q)t FD(;)g Fv(y)2849 1860 y Fp(\003)2887
1901 y Fv(;)g(!)t FD(\))49 b(+)g Fu(O)s FD(\()p Fv(")3374
1860 y Fq(2)3413 1901 y FD(\))109 2121 y(where)416 2096
y(\026)390 2121 y Fv(H)471 2136 y Fq(1)543 2121 y FD(is)33
b(the)g Ft(T)875 2085 y Fs(n)923 2121 y FD({a)m(v)m(erage)g(along)f
Fv(x)h FD(of)f Fv(H)1861 2136 y Fq(1)1933 2121 y FD(at)g
Fv(")c FD(=)f(0.)43 b(In)33 b(the)g(expansion)907 2316
y(\026)881 2341 y Fv(H)962 2356 y Fq(1)1140 2341 y FD(=)138
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2300 y Fp(\003)1629 2341 y Fv(;)g(!)t FD(\))49 b(+)h
Fv(\013)q FD(\()7 b(^)-56 b Fv(y)s FD(;)17 b Fv(y)2199
2300 y Fp(\003)2237 2341 y Fv(;)g(!)t FD(\))p Fv(p)49
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Fv(y)2853 2300 y Fp(\003)2891 2341 y Fv(;)g(!)t FD(\))p
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2437 y Fp(\003)1647 2474 y FD(\))p 1446 2518 240 4 v
1541 2609 a(2)1695 2541 y Fv(p)1744 2500 y Fq(2)1833
2541 y FD(+)1969 2474 y Fv(B)5 b FD(\()p Fv(y)2138 2437
y Fp(\003)2177 2474 y FD(\))p 1969 2518 246 4 v 2067
2609 a(2)2225 2541 y Fv(q)2272 2500 y Fq(2)2361 2541
y FD(+)49 b Fv(C)7 b FD(\()p Fv(y)2653 2500 y Fp(\003)2692
2541 y FD(\))p Fv(pq)53 b FD(+)d Fv(:)17 b(:)g(:)109
2792 y FD(w)m(e)43 b(ma)m(y)h(ha)m(v)m(e)g Fv(A)p FD(\()p
Fv(y)882 2756 y Fp(\003)920 2792 y FD(\))h Fu(\021)h
FD(0,)f(but)d(more)h(imp)s(ortan)m(tly)h Fu(j)p Fv(a)p
FD(\()p Fv(y)2408 2756 y Fp(\003)2446 2792 y FD(\))29
b(+)g Fv("A)p FD(\()p Fv(y)2827 2756 y Fp(\003)2865 2792
y FD(\))p Fu(j)42 b FD(is)i(still)f(b)s(ounded)g(from)109
2912 y(b)s(elo)m(w)38 b(on)g Ft(Y)p FD(.)59 b(Re-parametrising)c
Fv(!)40 b Fu(7!)d Fv(!)29 b FD(+)c Fv("D)2038 2927 y
Fq(^)-40 b Fs(y)2074 2912 y Fv(\021)t FD(\()7 b(^)-56
b Fv(y)s FD(;)17 b Fv(y)2311 2876 y Fp(\003)2349 2912
y Fv(;)g(!)t FD(\))54 b(the)38 b(expansion)h(of)f Fv(H)3379
2927 y Fs(")3453 2912 y FD(still)h(starts)109 3033 y(with)e
Fu(h)p Fv(!)t(;)22 b FD(^)-54 b Fv(y)r Fu(i)p FD(.)54
b(By)37 b(means)g(of)f(an)g Fv(")p FD({small)h(shear)g(transformation)f
(in)h Fv(p)f FD(w)m(e)h(get)g(rid)f(of)g(terms)h(that)109
3153 y(are)32 b(linear)h(in)g Fv(p)p FD(,)g(and)f(scaling)i
Fv(p)e FD(b)m(y)1492 3081 y Fu(p)p 1575 3081 46 4 v 72
x Fv(")g FD(w)m(e)h(arriv)m(e)h(at)783 3373 y Fv(H)864
3388 y Fs(")901 3373 y FD(\()p Fv(x;)24 b FD(^)-56 b
Fv(y)s(;)17 b(p;)g(q)t FD(;)g Fv(y)1369 3332 y Fp(\003)1407
3373 y Fv(;)g(!)t FD(\))82 b(=)g Fu(h)p Fv(!)t(;)23 b
FD(^)-55 b Fv(y)r Fu(i)50 b FD(+)g Fv(")p Fu(H)q FD(\()p
Fv(p;)17 b(q)t FD(;)g Fv(y)2612 3332 y Fp(\003)2649 3373
y Fv(;)g(!)t FD(\))49 b(+)g Fu(O)s FD(\()p Fv(")3136
3332 y Fq(2)3176 3373 y FD(\))109 3593 y(with)1189 3744
y Fu(H)q FD(\()p Fv(p;)17 b(q)t FD(;)g Fv(y)1548 3702
y Fp(\003)1586 3744 y Fv(;)g(!)t FD(\))82 b(=)1985 3676
y(~)-50 b Fv(a)p FD(\()p Fv(y)2125 3640 y Fp(\003)2163
3676 y FD(\))p 1984 3721 218 4 v 2068 3812 a(2)2211 3744
y Fv(p)2260 3702 y Fq(2)2349 3744 y FD(+)50 b Fv(V)2532
3759 y Fs(y)2569 3740 y Fm(\003)2609 3744 y FD(\()p Fv(q)t
FD(\))f Fv(;)109 3949 y FD(compare)33 b(with)g(\(4\).)109
4119 y(Here)38 b Fv(V)401 4134 y Fs(y)438 4115 y Fm(\003)516
4119 y FD(can)g(b)s(e)g(in)m(terpreted)h(as)f(an)g Fv(n)p
FD({parameter)g(family)g(of)f(1{dimensional)i(p)s(oten)m(tials,)h(and)
109 4239 y(critical)e(p)s(oin)m(ts)h Fv(q)785 4203 y
Fp(\003)862 4239 y FD(of)e Fv(V)1035 4254 y Fs(y)1072
4235 y Fm(\003)1151 4239 y FD(corresp)s(ond)h(to)g(in)m(v)-5
b(arian)m(t)38 b Fv(n)p FD({tori)g Ft(T)2554 4203 y Fs(n)2627
4239 y Fu(\002)27 b(f)p FD(\(0)p Fv(;)17 b FD(0)p Fv(;)g(q)3052
4203 y Fp(\003)3090 4239 y FD(;)g Fv(y)3186 4203 y Fp(\003)3224
4239 y Fv(;)g(!)t FD(\))p Fu(g)36 b FD(of)i(the)g(`in-)109
4360 y(termediate')i(in)m(tegrable)f(system)i(with)e(Hamiltonian)56
b Fu(H)2314 4375 y Fs(")2389 4360 y FD(=)38 b Fu(h)p
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Fu(H)17 b FD(.)62 b(The)40 b Fv(y)3363 4324 y Fp(\003)3439
4360 y Fu(2)f Ft(R)3616 4324 y Fs(n)3701 4360 y Fu(\031)f
Ft(Y)109 4480 y FD(around)31 b(whic)m(h)40 b(^)-56 b
Fv(y)35 b FD(is)d(lo)s(calised)g(has)g(the)g(c)m(haracter)h(of)e(a)g
(\(distinguished\))j(parameter;)e(let)g(us)g(mak)m(e)109
4601 y(this)h(explicit)h(b)m(y)g(writing)1779 4721 y
Fv(\026)55 b FD(:=)g Fv(y)2103 4680 y Fp(\003)2191 4721
y Fv(:)109 4895 y FD(While)34 b(critical)f(p)s(oin)m(ts)h(of)e(a)h
(single)h(p)s(oten)m(tial)f(are)g(generically)i(non-degenerate,)f(it)f
(is)h(generic)g(for)109 5016 y(the)27 b Fv(n)p FD({parameter)h(family)f
Fv(V)1188 5031 y Fs(\026)1261 5016 y FD(of)g(p)s(oten)m(tials)h(to)e
(encoun)m(ter)j(critical)e(p)s(oin)m(ts)h(up)f(to)g(co-dimension)h
Fv(n)p FD(.)109 5136 y(Note)40 b(that)h(this)g(amoun)m(ts)g(to)f(a)g
(genericit)m(y)j(condition)e(on)f(the)h(p)s(erturbation)g
Fv(H)3256 5151 y Fq(1)3335 5136 y FD(of)f Fv(H)3535 5151
y Fq(0)3575 5136 y FD(.)67 b(More)109 5256 y(precisely)-8
b(,)45 b(the)c Fv(\026)p FD({v)-5 b(alues)41 b(parametrising)g(a)f(p)s
(oten)m(tial)h Fv(V)2311 5271 y Fs(\026)2398 5256 y FD(with)h(a)e
(degenerate)i(critical)f(p)s(oin)m(t)g(of)109 5377 y(co-dimension)34
b Fv(k)h FD(form)d(an)h(\()p Fv(n)22 b Fu(\000)h Fv(k)s
FD(\){dimensional)34 b(submanifold)f(\003)2661 5392 y
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%%Page: 7 7
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y Fp(\003)3290 208 y Fl(of)g(order)g Fv(j)i(<)30 b(d)109
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y Fs(\026)1129 494 y Fm(\003)1169 498 y FD(\()p Fv(q)t
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y FD(\))2791 457 y Fs(d)p Fq(+1)2922 418 y Fn(\001)3764
498 y FD(\(8\))109 696 y Fl(with)40 b Fv(b)p FD(\()p
Fv(\026)476 660 y Fp(\003)516 696 y FD(\))g Fu(6)p FD(=)h(0)f
Fl(and)g FD(2)g Fu(\024)h Fv(d)g Fu(\024)g Fv(n)27 b
FD(+)h(2)39 b Fl(near)i(the)f(critical)h(p)s(oin)m(t)f
Fv(q)2733 660 y Fp(\003)2813 696 y Fl(of)f Fv(V)2988
711 y Fs(\026)3030 692 y Fm(\003)3071 696 y Fl(.)66 b(When)41
b Fv(d)f FD(=)h(2)f Fl(the)109 817 y(critical)35 b(p)s(oin)m(t)g
Fv(q)740 781 y Fp(\003)813 817 y Fl(is)g(non-degenerate)h(and)f
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781 y Fp(\003)2355 817 y FD(\))34 b Fl(is)h(a)g(non-degenerate)g
(equilibrium)i(of)109 937 y(the)g(one-degree-of-freedom)h(system)h(|)e
(a)g(saddle)h(if)g FD(~)-50 b Fv(ab)36 b(<)g FD(0)h Fl(and)g(a)g(cen)m
(tre)i(if)e(b)s(oth)g(co)s(e\016cien)m(ts)109 1058 y(ha)m(v)m(e)44
b(the)g(same)g(sign.)77 b(In)43 b(case)h Fv(d)i Fu(\025)h
FD(3)c Fl(the)g(equilibrium)j(is)e(parab)s(olic)f(and)g(it)h(is)f
(furthermore)109 1178 y(generic)d(for)g(the)g(family)g
Fv(V)1140 1193 y Fs(\026)1227 1178 y Fl(to)f(pro)m(vide)i(a)f(v)m
(ersal)h(unfolding)f(of)f(the)h(degenerate)h(critical)g(p)s(oin)m(t.)
109 1298 y(Also)33 b(this)g(genericit)m(y)h(condition)f(is)g(a)g
(condition)g(on)f(the)h(p)s(erturbation)g Fv(H)2955 1313
y Fq(1)2994 1298 y Fl(.)109 1507 y FD(Let)26 b(us)h(translate)g
(co-ordinates)g(to)f Fv(q)1499 1471 y Fp(\003)1566 1507
y FD(=)h(0)g(and)f(concen)m(trate)i(on)e(a)g(degenerate)i(critical)f(p)
s(oin)m(t)g(with)109 1627 y Fv(d)g Fu(\024)h Fv(n)23
b FD(+)f(1.)43 b(Then)664 1912 y Fu(H)q FD(\()p Fv(p;)17
b(q)t FD(;)g Fv(\026;)g(!)t FD(\))81 b(=)1428 1845 y(~)-50
b Fv(a)p FD(\()p Fv(\026)p FD(\))p 1427 1889 186 4 v
1495 1981 a(2)1622 1912 y Fv(p)1671 1871 y Fq(2)1761
1912 y FD(+)1893 1818 y(~)1896 1845 y Fv(b)q FD(\()p
Fv(\026)p FD(\))p 1896 1889 177 4 v 1945 1981 a Fv(d)p
FD(!)2082 1912 y Fv(q)2129 1871 y Fs(d)2219 1912 y FD(+)2354
1788 y Fs(d)p Fp(\000)p Fq(2)2345 1818 y Fn(X)2356 2027
y Fs(j)t Fq(=1)2516 1845 y Fv(c)2558 1860 y Fs(j)2594
1845 y FD(\()p Fv(\026)p FD(\))p 2516 1889 214 4 v 2586
1981 a Fv(j)6 b FD(!)2739 1912 y Fv(q)2786 1871 y Fs(j)2872
1912 y FD(+)49 b Fu(O)s FD(\()p Fv(q)3164 1871 y Fs(d)p
Fq(+1)3295 1912 y FD(\))109 2216 y(and)55 b Fu(H)405
2231 y Fs(")480 2216 y FD(=)38 b Fu(h)p Fv(!)t(;)22 b
FD(^)-54 b Fv(y)r Fu(i)26 b FD(+)g Fv(")p Fu(H)56 b FD(has)39
b(the)g(form)f(\(1)p Fv(:)p FD(4\))h(of)f([5])g(with)i
Fv(\025)2519 2231 y Fs(j)2593 2216 y FD(=)e Fv("c)2795
2231 y Fs(j)2831 2216 y FD(\()p Fv(\026)p FD(\).)61 b(Th)m(us)41
b(under)e(generic)109 2336 y(small)30 b(p)s(erturbation)g(the)g
(resonan)m(t)h(Lagrangean)e(torus)h(leads)g(to)g(the)g(whole)g
(bifurcation)g(scenario)109 2457 y(detailed)37 b(in)f([5].)54
b(This)37 b(amoun)m(ts)g(to)f(the)g(classical)i(hierarc)m(h)m(y)g(of)d
(the)i(cusp)s(oids)g([23,)f(3])g(unfolding)109 2577 y(the)30
b(singularities)h Fv(A)887 2592 y Fs(k)930 2577 y FD(,)f
Fv(k)h Fu(2)d Ft(N)p FD(,)j(that)e(are)h(Can)m(torised)h(b)m(y)g
(taking)f(out)g(the)g(dense)h(set)g(of)e(resonances)109
2697 y(men)m(tioned)34 b(b)s(efore)f(and)f(using)h(KAM)g(Theory)-8
b(.)109 2906 y Fo(Remark)38 b(2.2)49 b FD(Since)40 b
Fv(\026)f FD(=)h Fv(y)30 b Fu(\000)k FD(^)-56 b Fv(y)43
b FD(w)m(as)d(in)m(tro)s(duced)h(b)m(y)g(lo)s(calisation)e(the)h(r^)-49
b(ole)40 b(of)f(the)h(unfolding)109 3026 y(parameter)34
b Fv(\025)g FD(is)h(ultimately)g(pla)m(y)m(ed)g(b)m(y)g(the)g(action)f
Fv(y)j FD(conjugate)d(to)g(the)g(toral)g(angles,)h(pro)m(vided)109
3147 y(that)25 b Fv(c)j FD(:)f Fv(\026)h Fu(7!)f Fv(c)p
FD(\()p Fv(\026)p FD(\))e(is)h(at)f Fv(\026)j FD(=)f(0)f(a)f
(submersion)i(from)f Ft(R)2194 3111 y Fs(n)2266 3147
y FD(to)f Ft(R)2450 3111 y Fs(d)p Fp(\000)p Fq(2)2581
3147 y FD(.)41 b(The)27 b(tori)e Ft(T)3086 3111 y Fs(n)3141
3147 y Fu(\002)8 b(f)p FD(\(0)p Fv(;)17 b FD(0)p Fv(;)g(q)3547
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0 g
0.5 w
[ ] 0 d
154.308 57.278 m
154.71 57.242 L
155.11 57.212 L
155.512 57.188 L
155.912 57.168 L
156.312 57.154 L
156.714 57.146 L
157.114 57.142 L
157.516 57.146 L
157.916 57.154 L
158.316 57.168 L
158.718 57.188 L
159.118 57.214 L
159.52 57.246 L
159.92 57.284 L
160.2 57.314 L
160.32 57.328 L
160.722 57.38 L
161.122 57.438 L
161.524 57.504 L
161.924 57.576 L
162.324 57.654 L
162.61 57.716 L
162.726 57.74 L
163.126 57.834 L
163.528 57.936 L
163.928 58.046 L
164.172 58.116 L
164.328 58.162 L
164.73 58.288 L
165.13 58.422 L
165.4 58.518 L
165.532 58.564 L
165.932 58.716 L
166.332 58.876 L
166.434 58.918 L
166.734 59.044 L
167.134 59.224 L
167.338 59.318 L
167.536 59.412 L
167.936 59.61 L
168.146 59.72 L
168.336 59.82 L
168.738 60.04 L
168.88 60.12 L
169.138 60.27 L
169.54 60.512 L
169.556 60.522 L
169.94 60.764 L
170.18 60.922 L
S
170.18 60.922 m
170.34 61.03 L
170.742 61.306 L
170.764 61.322 L
171.142 61.596 L
171.312 61.724 L
171.544 61.9 L
171.828 62.124 L
171.944 62.216 L
172.318 62.526 L
172.344 62.548 L
172.746 62.894 L
172.782 62.926 L
173.146 63.254 L
173.224 63.326 L
173.548 63.632 L
173.646 63.728 L
173.948 64.024 L
174.05 64.128 L
174.348 64.434 L
174.438 64.53 L
174.75 64.864 L
174.81 64.93 L
175.15 65.31 L
175.168 65.33 L
175.512 65.732 L
175.552 65.778 L
175.844 66.132 L
175.952 66.266 L
176.164 66.534 L
176.352 66.774 L
176.474 66.934 L
176.754 67.308 L
176.774 67.334 L
177.064 67.736 L
177.154 67.864 L
177.344 68.136 L
177.556 68.448 L
177.616 68.538 L
177.878 68.938 L
177.956 69.058 L
178.134 69.338 L
178.356 69.698 L
178.382 69.74 L
178.624 70.14 L
178.758 70.368 L
178.858 70.542 L
179.086 70.942 L
179.158 71.074 L
179.306 71.342 L
179.522 71.744 L
S
179.522 71.744 m
179.56 71.814 L
179.73 72.144 L
179.934 72.546 L
179.96 72.596 L
180.132 72.946 L
180.326 73.346 L
180.36 73.422 L
180.514 73.748 L
180.696 74.148 L
180.762 74.294 L
180.874 74.55 L
181.048 74.95 L
181.162 75.22 L
181.216 75.35 L
181.382 75.752 L
181.542 76.152 L
181.564 76.208 L
181.698 76.554 L
181.85 76.954 L
181.964 77.262 L
181.998 77.354 L
182.142 77.756 L
182.284 78.156 L
182.364 78.394 L
182.42 78.558 L
182.554 78.958 L
182.684 79.358 L
182.766 79.618 L
182.81 79.76 L
182.934 80.16 L
183.052 80.562 L
183.166 80.95 L
183.17 80.962 L
183.282 81.362 L
183.394 81.764 L
183.5 82.164 L
183.568 82.42 L
183.604 82.566 L
183.706 82.966 L
183.804 83.366 L
183.9 83.768 L
183.968 84.06 L
183.992 84.168 L
184.082 84.57 L
184.17 84.97 L
184.254 85.37 L
184.336 85.772 L
184.368 85.934 L
184.416 86.172 L
184.492 86.574 L
S
184.492 86.574 m
184.566 86.974 L
184.638 87.374 L
184.708 87.776 L
184.77 88.15 L
184.774 88.176 L
184.838 88.578 L
184.9 88.978 L
184.96 89.378 L
185.016 89.78 L
185.07 90.18 L
185.122 90.582 L
185.17 90.96 L
185.172 90.982 L
185.22 91.382 L
185.266 91.784 L
185.31 92.184 L
185.35 92.586 L
185.388 92.986 L
185.426 93.386 L
185.46 93.788 L
185.492 94.188 L
185.522 94.59 L
185.548 94.99 L
185.572 95.338 L
185.574 95.39 L
185.598 95.792 L
185.618 96.192 L
185.638 96.594 L
185.654 96.994 L
185.67 97.394 L
185.682 97.796 L
185.692 98.196 L
185.702 98.598 L
185.708 98.998 L
185.712 99.398 L
185.714 99.8 L
185.714 100.2 L
185.712 100.602 L
185.708 101.002 L
185.702 101.402 L
185.692 101.804 L
185.682 102.204 L
185.67 102.606 L
185.654 103.006 L
185.638 103.406 L
185.618 103.808 L
185.598 104.208 L
185.574 104.61 L
185.572 104.662 L
185.548 105.01 L
S
185.548 105.01 m
185.522 105.41 L
185.492 105.812 L
185.46 106.212 L
185.426 106.614 L
185.388 107.014 L
185.35 107.414 L
185.31 107.816 L
185.266 108.216 L
185.22 108.618 L
185.172 109.018 L
185.17 109.04 L
185.122 109.418 L
185.07 109.82 L
185.016 110.22 L
184.96 110.622 L
184.9 111.022 L
184.838 111.422 L
184.774 111.824 L
184.77 111.85 L
184.708 112.224 L
184.638 112.626 L
184.566 113.026 L
184.492 113.426 L
184.416 113.828 L
184.368 114.066 L
184.336 114.228 L
184.254 114.63 L
184.17 115.03 L
184.082 115.43 L
183.992 115.832 L
183.968 115.94 L
183.9 116.232 L
183.804 116.634 L
183.706 117.034 L
183.604 117.434 L
183.568 117.58 L
183.5 117.836 L
183.394 118.236 L
183.282 118.638 L
183.17 119.038 L
183.166 119.05 L
183.052 119.438 L
182.934 119.84 L
182.81 120.24 L
182.766 120.382 L
182.684 120.642 L
182.554 121.042 L
182.42 121.442 L
182.364 121.606 L
182.284 121.844 L
S
182.284 121.844 m
182.142 122.244 L
181.998 122.646 L
181.964 122.738 L
181.85 123.046 L
181.698 123.446 L
181.564 123.792 L
181.542 123.848 L
181.382 124.248 L
181.216 124.65 L
181.162 124.78 L
181.048 125.05 L
180.874 125.45 L
180.762 125.706 L
180.696 125.852 L
180.514 126.252 L
180.36 126.578 L
180.326 126.654 L
180.132 127.054 L
179.96 127.404 L
179.934 127.454 L
179.73 127.856 L
179.56 128.186 L
179.522 128.256 L
179.306 128.658 L
179.158 128.926 L
179.086 129.058 L
178.858 129.458 L
178.758 129.632 L
178.624 129.86 L
178.382 130.26 L
178.356 130.302 L
178.134 130.662 L
177.956 130.942 L
177.878 131.062 L
177.616 131.462 L
177.556 131.552 L
177.344 131.864 L
177.154 132.136 L
177.064 132.264 L
176.774 132.666 L
176.754 132.692 L
176.474 133.066 L
176.352 133.226 L
176.164 133.466 L
175.952 133.734 L
175.844 133.868 L
175.552 134.222 L
175.512 134.268 L
175.168 134.67 L
175.15 134.69 L
S
175.15 134.69 m
174.81 135.07 L
174.75 135.136 L
174.438 135.47 L
174.348 135.566 L
174.05 135.872 L
173.948 135.976 L
173.646 136.272 L
173.548 136.368 L
173.224 136.674 L
173.146 136.746 L
172.782 137.074 L
172.746 137.106 L
172.344 137.452 L
172.318 137.474 L
171.944 137.784 L
171.828 137.876 L
171.544 138.1 L
171.312 138.276 L
171.142 138.404 L
170.764 138.678 L
170.742 138.694 L
170.34 138.97 L
170.18 139.078 L
169.94 139.236 L
169.556 139.478 L
169.54 139.488 L
169.138 139.73 L
168.88 139.88 L
168.738 139.96 L
168.336 140.18 L
168.146 140.28 L
167.936 140.39 L
167.536 140.588 L
167.338 140.682 L
167.134 140.776 L
166.734 140.956 L
166.434 141.082 L
166.332 141.124 L
165.932 141.284 L
165.532 141.436 L
165.4 141.482 L
165.13 141.578 L
164.73 141.712 L
164.328 141.838 L
164.172 141.884 L
163.928 141.954 L
163.528 142.064 L
163.126 142.166 L
162.726 142.26 L
162.61 142.284 L
S
162.61 142.284 m
162.324 142.346 L
161.924 142.424 L
161.524 142.496 L
161.122 142.562 L
160.722 142.62 L
160.32 142.672 L
160.2 142.686 L
159.92 142.716 L
159.52 142.754 L
159.118 142.786 L
158.718 142.812 L
158.316 142.832 L
157.916 142.846 L
157.516 142.854 L
157.114 142.858 L
156.714 142.854 L
156.312 142.846 L
155.912 142.832 L
155.512 142.812 L
155.11 142.788 L
154.71 142.758 L
154.308 142.722 L
153.932 142.686 L
153.908 142.682 L
153.508 142.638 L
153.106 142.588 L
152.706 142.534 L
152.304 142.476 L
151.904 142.412 L
151.504 142.346 L
151.164 142.284 L
151.102 142.274 L
150.702 142.196 L
150.3 142.116 L
149.9 142.032 L
149.498 141.942 L
149.244 141.884 L
149.098 141.85 L
148.698 141.752 L
148.296 141.652 L
147.896 141.548 L
147.656 141.482 L
147.494 141.438 L
147.094 141.326 L
146.694 141.212 L
146.292 141.092 L
146.26 141.082 L
145.892 140.968 L
145.49 140.842 L
145.09 140.712 L
S
145.09 140.712 m
144.994 140.682 L
144.69 140.58 L
144.288 140.444 L
143.888 140.304 L
143.822 140.28 L
143.486 140.16 L
143.086 140.014 L
142.724 139.88 L
142.686 139.866 L
142.284 139.714 L
141.884 139.558 L
141.682 139.478 L
141.482 139.4 L
141.082 139.238 L
140.69 139.078 L
140.682 139.074 L
140.28 138.908 L
139.88 138.738 L
139.736 138.678 L
139.478 138.566 L
139.078 138.392 L
138.818 138.276 L
138.678 138.214 L
138.276 138.034 L
137.93 137.876 L
137.876 137.852 L
137.474 137.666 L
137.074 137.478 L
137.066 137.474 L
136.674 137.288 L
136.272 137.096 L
136.228 137.074 L
135.872 136.902 L
135.47 136.704 L
135.408 136.674 L
135.07 136.506 L
134.67 136.304 L
134.608 136.272 L
134.268 136.1 L
133.868 135.894 L
133.824 135.872 L
133.466 135.686 L
133.066 135.476 L
133.056 135.47 L
132.666 135.264 L
132.302 135.07 L
132.264 135.05 L
131.864 134.834 L
131.56 134.67 L
131.462 134.616 L
S
131.462 134.616 m
131.062 134.396 L
130.83 134.268 L
130.662 134.176 L
130.26 133.952 L
130.11 133.868 L
129.86 133.726 L
129.458 133.5 L
129.402 133.466 L
129.058 133.272 L
128.7 133.066 L
128.658 133.04 L
128.256 132.81 L
128.01 132.666 L
127.856 132.576 L
127.454 132.34 L
127.326 132.264 L
127.054 132.104 L
126.654 131.866 L
126.65 131.864 L
126.252 131.626 L
125.98 131.462 L
125.852 131.386 L
125.45 131.144 L
125.318 131.062 L
125.05 130.9 L
124.66 130.662 L
124.65 130.654 L
124.248 130.408 L
124.01 130.26 L
123.848 130.16 L
123.446 129.912 L
123.364 129.86 L
123.046 129.662 L
122.722 129.458 L
122.646 129.41 L
122.244 129.158 L
122.086 129.058 L
121.844 128.904 L
121.454 128.658 L
121.442 128.65 L
121.042 128.394 L
120.826 128.256 L
120.642 128.138 L
120.24 127.88 L
120.202 127.856 L
119.84 127.622 L
119.582 127.454 L
119.438 127.362 L
119.038 127.102 L
118.964 127.054 L
S
118.964 127.054 m
118.638 126.84 L
118.35 126.654 L
118.236 126.578 L
117.836 126.316 L
117.738 126.252 L
117.434 126.052 L
117.13 125.852 L
117.034 125.788 L
116.634 125.524 L
116.524 125.45 L
116.232 125.258 L
115.92 125.05 L
115.832 124.99 L
115.43 124.724 L
115.32 124.65 L
115.03 124.456 L
114.72 124.248 L
114.63 124.188 L
114.228 123.92 L
114.122 123.848 L
113.828 123.65 L
113.526 123.446 L
113.426 123.38 L
113.026 123.11 L
112.93 123.046 L
112.626 122.84 L
112.338 122.646 L
112.224 122.57 L
111.824 122.298 L
111.744 122.244 L
111.422 122.026 L
111.154 121.844 L
111.022 121.754 L
110.622 121.482 L
110.562 121.442 L
110.22 121.21 L
109.974 121.042 L
109.82 120.938 L
109.418 120.664 L
109.384 120.642 L
109.018 120.392 L
108.796 120.24 L
108.618 120.12 L
108.216 119.846 L
108.206 119.84 L
107.816 119.574 L
107.618 119.438 L
107.414 119.3 L
107.03 119.038 L
107.014 119.028 L
S
107.014 119.028 m
106.614 118.754 L
106.442 118.638 L
106.212 118.482 L
105.852 118.236 L
105.812 118.208 L
105.41 117.936 L
105.264 117.836 L
105.01 117.664 L
104.674 117.434 L
104.61 117.392 L
104.208 117.12 L
104.082 117.034 L
103.808 116.848 L
103.492 116.634 L
103.406 116.576 L
103.006 116.304 L
102.898 116.232 L
102.606 116.034 L
102.306 115.832 L
102.204 115.764 L
101.804 115.494 L
101.71 115.43 L
101.402 115.224 L
101.114 115.03 L
101.002 114.956 L
100.602 114.688 L
100.514 114.63 L
100.2 114.42 L
99.914 114.228 L
99.8 114.152 L
99.398 113.886 L
99.312 113.828 L
98.998 113.62 L
98.706 113.426 L
98.598 113.354 L
98.196 113.09 L
98.1 113.026 L
97.796 112.826 L
97.488 112.626 L
97.394 112.564 L
96.994 112.302 L
96.876 112.224 L
96.594 112.04 L
96.258 111.824 L
96.192 111.78 L
95.792 111.522 L
95.638 111.422 L
95.39 111.264 L
95.014 111.022 L
94.99 111.006 L
S
94.99 111.006 m
94.59 110.75 L
94.386 110.622 L
94.188 110.496 L
93.788 110.242 L
93.754 110.22 L
93.386 109.99 L
93.116 109.82 L
92.986 109.738 L
92.586 109.488 L
92.474 109.418 L
92.184 109.24 L
91.824 109.018 L
91.784 108.992 L
91.382 108.746 L
91.17 108.618 L
90.982 108.502 L
90.582 108.26 L
90.508 108.216 L
90.18 108.02 L
89.84 107.816 L
89.78 107.78 L
89.378 107.542 L
89.164 107.414 L
88.978 107.306 L
88.578 107.072 L
88.478 107.014 L
88.176 106.84 L
87.784 106.614 L
87.776 106.608 L
87.374 106.38 L
87.078 106.212 L
86.974 106.154 L
86.574 105.93 L
86.362 105.812 L
86.172 105.706 L
85.772 105.486 L
85.632 105.41 L
85.37 105.268 L
84.97 105.054 L
84.888 105.01 L
84.57 104.84 L
84.168 104.63 L
84.13 104.61 L
83.768 104.422 L
83.366 104.216 L
83.352 104.208 L
82.966 104.014 L
82.566 103.814 L
82.554 103.808 L
82.164 103.616 L
S
82.164 103.616 m
81.764 103.422 L
81.73 103.406 L
81.362 103.232 L
80.962 103.044 L
80.88 103.006 L
80.562 102.86 L
80.16 102.678 L
79.996 102.606 L
79.76 102.502 L
79.358 102.328 L
79.072 102.204 L
78.958 102.158 L
78.558 101.992 L
78.156 101.828 L
78.094 101.804 L
77.756 101.672 L
77.354 101.52 L
77.048 101.402 L
76.954 101.37 L
76.554 101.23 L
76.152 101.09 L
75.904 101.002 L
75.752 100.964 L
75.35 100.848 L
74.95 100.72 L
74.6 100.602 L
74.55 100.588 L
74.148 100.478 L
73.748 100.378 L
73.346 100.284 L
72.946 100.2 L
72.946 100.2 L
72.946 99.8 L
72.946 99.8 L
73.346 99.716 L
73.748 99.622 L
74.148 99.522 L
74.55 99.412 L
74.6 99.398 L
74.95 99.28 L
75.35 99.152 L
75.752 99.036 L
75.904 98.998 L
76.152 98.91 L
76.554 98.77 L
76.954 98.63 L
77.048 98.598 L
77.354 98.48 L
77.756 98.328 L
78.094 98.196 L
S
78.094 98.196 m
78.156 98.172 L
78.558 98.008 L
78.958 97.842 L
79.072 97.796 L
79.358 97.672 L
79.76 97.498 L
79.996 97.394 L
80.16 97.322 L
80.562 97.14 L
80.88 96.994 L
80.962 96.956 L
81.362 96.768 L
81.73 96.594 L
81.764 96.578 L
82.164 96.384 L
82.554 96.192 L
82.566 96.186 L
82.966 95.986 L
83.352 95.792 L
83.366 95.784 L
83.768 95.578 L
84.13 95.39 L
84.168 95.37 L
84.57 95.16 L
84.888 94.99 L
84.97 94.946 L
85.37 94.732 L
85.632 94.59 L
85.772 94.514 L
86.172 94.294 L
86.362 94.188 L
86.574 94.07 L
86.974 93.846 L
87.078 93.788 L
87.374 93.62 L
87.776 93.392 L
87.784 93.386 L
88.176 93.16 L
88.478 92.986 L
88.578 92.928 L
88.978 92.694 L
89.164 92.586 L
89.378 92.458 L
89.78 92.22 L
89.84 92.184 L
90.18 91.98 L
90.508 91.784 L
90.582 91.74 L
90.982 91.498 L
91.17 91.382 L
S
91.17 91.382 m
91.382 91.254 L
91.784 91.008 L
91.824 90.982 L
92.184 90.76 L
92.474 90.582 L
92.586 90.512 L
92.986 90.262 L
93.116 90.18 L
93.386 90.01 L
93.754 89.78 L
93.788 89.758 L
94.188 89.504 L
94.386 89.378 L
94.59 89.25 L
94.99 88.994 L
95.014 88.978 L
95.39 88.736 L
95.638 88.578 L
95.792 88.478 L
96.192 88.22 L
96.258 88.176 L
96.594 87.96 L
96.876 87.776 L
96.994 87.698 L
97.394 87.436 L
97.488 87.374 L
97.796 87.174 L
98.1 86.974 L
98.196 86.91 L
98.598 86.646 L
98.706 86.574 L
98.998 86.38 L
99.312 86.172 L
99.398 86.114 L
99.8 85.848 L
99.914 85.772 L
100.2 85.58 L
100.514 85.37 L
100.602 85.312 L
101.002 85.044 L
101.114 84.97 L
101.402 84.776 L
101.71 84.57 L
101.804 84.506 L
102.204 84.236 L
102.306 84.168 L
102.606 83.966 L
102.898 83.768 L
103.006 83.696 L
103.406 83.424 L
S
103.406 83.424 m
103.492 83.366 L
103.808 83.152 L
104.082 82.966 L
104.208 82.88 L
104.61 82.608 L
104.674 82.566 L
105.01 82.336 L
105.264 82.164 L
105.41 82.064 L
105.812 81.792 L
105.852 81.764 L
106.212 81.518 L
106.442 81.362 L
106.614 81.246 L
107.014 80.972 L
107.03 80.962 L
107.414 80.7 L
107.618 80.562 L
107.816 80.426 L
108.206 80.16 L
108.216 80.154 L
108.618 79.88 L
108.796 79.76 L
109.018 79.608 L
109.384 79.358 L
109.418 79.336 L
109.82 79.062 L
109.974 78.958 L
110.22 78.79 L
110.562 78.558 L
110.622 78.518 L
111.022 78.246 L
111.154 78.156 L
111.422 77.974 L
111.744 77.756 L
111.824 77.702 L
112.224 77.43 L
112.338 77.354 L
112.626 77.16 L
112.93 76.954 L
113.026 76.89 L
113.426 76.62 L
113.526 76.554 L
113.828 76.35 L
114.122 76.152 L
114.228 76.08 L
114.63 75.812 L
114.72 75.752 L
115.03 75.544 L
115.32 75.35 L
S
115.32 75.35 m
115.43 75.276 L
115.832 75.01 L
115.92 74.95 L
116.232 74.742 L
116.524 74.55 L
116.634 74.476 L
117.034 74.212 L
117.13 74.148 L
117.434 73.948 L
117.738 73.748 L
117.836 73.684 L
118.236 73.422 L
118.35 73.346 L
118.638 73.16 L
118.964 72.946 L
119.038 72.898 L
119.438 72.638 L
119.582 72.546 L
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120.202 72.144 L
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120.642 71.862 L
120.826 71.744 L
121.042 71.606 L
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121.454 71.342 L
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122.086 70.942 L
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122.722 70.542 L
123.046 70.338 L
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123.446 70.088 L
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124.01 69.74 L
124.248 69.592 L
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124.66 69.338 L
125.05 69.1 L
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125.45 68.856 L
125.852 68.614 L
125.98 68.538 L
126.252 68.374 L
126.65 68.136 L
126.654 68.134 L
127.054 67.896 L
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127.454 67.66 L
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128.01 67.334 L
128.256 67.19 L
128.658 66.96 L
128.7 66.934 L
129.058 66.728 L
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139.736 61.322 L
139.88 61.262 L
140.28 61.092 L
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131.318 113.132 L
131.314 113.124 L
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138.972 78.788 L
139.394 78.456 L
141.414 76.982 L
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145.11 74.748 L
145.454 74.568 L
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149.76 72.728 L
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149.494 43.54 L
151.516 43.238 L
153.536 43.018 L
155.556 42.89 L
157.576 42.86 L
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28.282 57.312 L
29.136 56.566 L
30.304 55.604 L
31.692 54.546 L
32.324 54.094 L
34.344 52.754 L
34.714 52.526 L
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38.384 50.51 L
38.394 50.506 L
40.404 49.572 L
42.424 48.74 L
43.094 48.484 L
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48.484 46.772 L
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50.506 46.266 L
52.526 45.82 L
54.546 45.432 L
56.566 45.094 L
58.586 44.802 L
60.606 44.552 L
61.57 44.444 L
62.626 44.336 L
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64.646 68.61 m
66.666 68.34 L
68.686 68.116 L
70.708 67.932 L
72.728 67.784 L
74.748 67.666 L
76.768 67.574 L
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88.888 67.352 L
90.91 67.346 L
92.93 67.342 L
94.95 67.34 L
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101.01 67.34 L
103.03 67.34 L
105.05 67.34 L
107.07 67.342 L
109.09 67.346 L
111.112 67.352 L
113.132 67.364 L
115.152 67.382 L
117.172 67.41 L
119.192 67.448 L
121.212 67.502 L
123.232 67.574 L
125.252 67.666 L
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131.314 68.116 L
133.334 68.34 L
135.354 68.61 L
135.864 68.686 L
137.374 68.934 L
139.394 69.32 L
141.414 69.776 L
143.434 70.314 L
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145.454 70.942 L
147.474 71.678 L
149.494 72.54 L
149.898 72.728 L
151.516 73.544 L
153.536 74.724 L
153.572 74.748 L
155.556 76.114 L
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155.556 76.114 m
156.398 76.768 L
157.576 77.766 L
158.66 78.788 L
159.596 79.76 L
160.512 80.808 L
161.616 82.224 L
162.044 82.828 L
163.318 84.848 L
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164.372 86.868 L
165.234 88.888 L
165.656 90.054 L
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166.47 92.93 L
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167.126 96.97 L
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167.126 103.03 L
166.866 105.05 L
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143.434 129.686 L
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139.394 130.68 L
137.374 131.066 L
135.864 131.314 L
135.354 131.39 L
133.334 131.66 L
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133.334 131.66 m
131.314 131.884 L
129.292 132.068 L
127.272 132.216 L
125.252 132.334 L
123.232 132.426 L
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50.506 127.46 L
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48.484 126.456 L
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44.444 123.886 L
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42.424 122.234 L
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42.424 122.234 m
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38.384 117.776 L
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36.682 115.152 L
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58.586 97.394 L
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60.606 94.092 m
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100. 100. 1. dot
97.2 156.4 m
102.8 156.4 L
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97.8 157.65 m
102.8 156.4 L
97.8 155.15 L
99.3 156.4 L
F
97.8 157.65 m
102.8 156.4 L
97.8 155.15 L
99.3 156.4 L
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97.6 132.4 m
102.4 132.4 L
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97.4 133.65 m
102.4 132.4 L
97.4 131.15 L
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F
97.4 133.65 m
102.4 132.4 L
97.4 131.15 L
98.9 132.4 L
97.4 133.65 L
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98. 112.8 m
102. 112.8 L
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97. 114.05 m
102. 112.8 L
97. 111.55 L
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F
97. 114.05 m
102. 112.8 L
97. 111.55 L
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89.448 117.914 L
88.754 118.592 L
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87.722 119.598 L
87.438 119.876 L
86.686 120.604 L
86.432 120.85 L
85.644 121.608 L
85.428 121.816 L
84.594 122.614 L
84.422 122.778 L
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77.386 129.284 L
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69.346 136.056 L
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68.342 136.838 L
67.336 137.604 L
67.224 137.688 L
66.332 138.352 L
65.864 138.694 L
65.326 139.08 L
64.456 139.698 L
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64.456 139.698 m
64.322 139.792 L
63.316 140.482 L
62.99 140.704 L
62.312 141.154 L
61.454 141.708 L
61.306 141.802 L
60.302 142.43 L
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59.296 143.034 L
58.292 143.614 L
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57.286 144.168 L
56.282 144.698 L
56.23 144.724 L
55.276 145.198 L
54.272 145.672 L
54.148 145.728 L
53.266 146.116 L
52.262 146.53 L
51.738 146.734 L
51.256 146.912 L
50.252 147.262 L
49.246 147.576 L
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45.226 148.456 L
44.222 148.574 L
43.216 148.646 L
42.212 148.672 L
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40.202 148.572 L
39.196 148.442 L
38.19 148.254 L
37.186 148.004 L
36.322 147.738 L
36.18 147.69 L
35.176 147.308 L
34.17 146.852 L
33.934 146.734 L
33.166 146.318 L
32.206 145.728 L
32.16 145.698 L
31.156 144.99 L
30.81 144.724 L
30.15 144.182 L
29.624 143.718 L
29.146 143.27 L
28.59 142.714 L
S
28.59 142.714 m
28.14 142.238 L
27.668 141.708 L
27.136 141.076 L
26.836 140.704 L
26.13 139.772 L
26.078 139.698 L
25.382 138.694 L
25.126 138.302 L
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18.102 80.402 L
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18.778 77.386 L
19.032 76.382 L
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30.81 55.276 L
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32.16 54.302 L
32.206 54.272 L
33.166 53.682 L
33.934 53.266 L
34.17 53.148 L
35.176 52.692 L
36.18 52.31 L
36.322 52.262 L
37.186 51.996 L
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38.384 34.79 L
40.404 34.57 L
42.424 34.51 L
44.444 34.6 L
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66.666 41.932 L
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89.082 52.526 L
90.91 53.186 L
92.93 53.852 L
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95.332 54.546 L
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98.99 55.376 L
101.01 55.712 L
103.03 55.96 L
105.05 56.116 L
107.07 56.18 L
109.09 56.158 L
111.112 56.05 L
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151.516 48.256 L
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173.256 62.626 L
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175.758 67.846 L
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177.778 73.598 L
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179.544 80.808 L
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y Fv(;)17 b(:)g(:)g(:)f(;)h(I)3219 2739 y Fq(4)3258 2724
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3350 y(to)31 b(Lagrangean)h(tori)g(and)g(equilibria)i(to)d
(3{dimensional)j(tori.)43 b(In)32 b(the)h(case)g(of)e(a)h(cen)m(ter)i
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(o\))g(remaining)g(cases.)109 3615 y(W)-8 b(e)22 b(recall)g(that)g
Fv(\026)27 b Fu(7!)g Fv(\025)p FD(\()p Fv(\026)p FD(\))21
b(is)i(a)e(\(lo)s(cal\))g(submersion.)42 b(Therefore)23
b(Can)m(torisation)g(in)f(the)g(\()p Fv(\026)3528 3630
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3735 y(direction)33 b(amoun)m(ts)h(to)e(the)h(follo)m(wing.)228
3935 y(1.)49 b(W)-8 b(e)33 b(b)s(egin)f(with)i(the)f(cases)h(corresp)s
(onding)f(to)f(parab)s(olic)h(tori.)394 4137 y(\(a\))48
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4860 y(whic)m(h)34 b(corresp)s(onds)g(to)e(an)h(op)s(en)g
(3{dimensional)g(set.)45 b(Can)m(torisation)33 b(leads)h(to)e(a)h
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(parametrise)h(elliptic)f(tori,)g(observing)h(that)e(in)g(b)s(et)m(w)m
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(onds)h(to)e(t)m(w)m(o)h(elliptic)h(tori,)e(and)h(in)g(the)g(other)f
(region)h(only)g(to)f(one.)1974 5778 y(8)p eop end
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367 y(\(b\))49 b(In)33 b(the)g(former)g(case)g(Can)m(torisation)g
(leads)h(to)e(t)m(w)m(o)h(la)m(y)m(ers)i(of)d(Can)m(tor)g(dust.)109
567 y(As)g(usual,)h(Can)m(torisation)g(of)e(the)i(librational)f
(Lagrangean)f(tori)h(tak)m(es)h(place)g(along)e(a)h(Can)m(tor)g(set)109
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1542 y Fs(\026)3761 1527 y FD(,)h Fv(\026)109 1647 y
FD(\014xed,)f(assumes)h(minim)m(um)e(and)g(maxim)m(um.)62
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1662 y Fq(1)3391 1647 y FD(for)g(these)h(to)109 1767
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1888 y(the)h(form)f(\(8\))g(with)h Fv(d)g FD(ev)m(en)h(and)f
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2008 y(let)i(us)g(denote)h(the)g(latter)e(b)m(y)i Fv(q)1327
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m(e)f(concen)m(trate)h(on)f(~)-51 b Fv(a)q FD(\()p Fv(\026)p
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y(alw)m(a)m(ys)h(b)s(e)f(ac)m(hiev)m(ed)j(b)m(y)d(rev)m(ersing)i(time)f
(if)f(necessary\).)62 b(Then)39 b(the)f(maxim)m(um)i
Fv(q)3309 2092 y Fp(\003)3386 2128 y FD(corresp)s(onds)109
2249 y(to)h(a)g(`h)m(yp)s(erb)s(olic')h(t)m(yp)s(e)h(torus)e
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b FD(replaced)34 b(b)m(y)f Fv(n)p FD(.)109 2633 y(The)f(p)s(ersistence)
i(of)e(at)f(least)h(one)g Fv(n)p FD({torus)g(from)g(the)g
Fv(H)2272 2648 y Fq(0)2311 2633 y FD({resonan)m(t)h Ft(T)2819
2597 y Fs(n)2887 2633 y Fu(\002)20 b(f)p FD(\(0)p Fv(;)d
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y FD(for)31 b(Dio-)109 2754 y(phan)m(tine)h Fv(!)i FD(had)d(already)g
(b)s(een)h(established)g(in)g([13)o(],)f(and)g(without)h(an)m(y)f
(genericit)m(y)i(condition)e(on)109 2874 y(the)41 b(p)s(erturbation.)71
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3115 y(Can)m(torised)g(bifurcation)f(scenario)h(of)e(the)h(corresp)s
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s(e)109 3235 y(obtained)g(without)g(genericit)m(y)h(conditions.)109
3402 y(The)42 b(minima)f Fv(q)721 3417 y Fp(\003)802
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(non-degenerate)g(case)f(these)i(corresp)s(ond)f(to)e(el-)109
3523 y(liptic)e Fv(n)p FD({tori,)i(whence)f(normal-in)m(ternal)g
(resonances)h(ha)m(v)m(e)f(to)f(b)s(e)g(a)m(v)m(oided)i(as)e(w)m(ell.)
61 b(Therefore,)109 3643 y(p)s(ersistence)29 b(of)d(a)h(second)h
Fv(n)p FD({torus)f(is)h(obtained)f(in)g([14])g(only)g(on)g(a)g(smaller)
h(\(though)f(still)g(measure-)109 3763 y(theoretically)i(large\))f
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(ersistence)i(of)d(a)h(second)109 4486 y(family)k(of)f(in)m(v)-5
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(tori)109 4822 y Ft(T)175 4786 y Fs(n)247 4822 y Fu(\002)26
b(f)p FD(\(0)p Fv(;)17 b FD(0)p Fv(;)g(q)671 4786 y Fp(\003)709
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b(extra)h(\(external\))g(parameters)f Fv(\027)50 b FD(to)42
b(pro)m(vide)i(a)f(v)m(ersal)h(unfolding.)75 b(The)43
b(p)s(erturb)s(ed)109 5062 y(system)36 b(then)e(displa)m(ys)i(again)d
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(the)f(original)109 5183 y(p)s(erturb)s(ed)43 b(system)j(as)d(a)g
(subsystem.)78 b(Ho)m(w)m(ev)m(er,)48 b(w)m(e)c(cannot)f(exp)s(ect)i
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Fe(#144,)f(p.)i(1)g({)f(52)f(\(1974\))109 4249 y([22])48
b Fc(J.)30 b(P\177)-42 b(osc)n(hel)30 b(:)74 b Fe(In)n(tegrabilit)n(y)
30 b(of)h(Hamiltonian)g(Systems)g(on)f(Can)n(tor)g(Sets)h(;)i
FC(Comm.)h(Pur)l(e)e(Appl.)i(Math.)f Fb(35)p Fe(,)287
4348 y(p.)27 b(653)g({)g(696)f(\(1982\))109 4495 y([23])48
b Fc(R.)25 b(Thom)h(:)61 b FC(Structur)l(al)27 b(Stability)i(and)f
(Morpho)l(genesis.)j(A)n(n)c(Outline)g(of)i(a)f(Gener)l(al)h(The)l(ory)
g(of)g(Mo)l(dels)p Fe(,)e(2nd)287 4595 y(ed,;)g(Addison-W)-7
b(esley)28 b(\(1989\))109 4741 y([24])48 b Fc(M.B.)26
b(Sevryuk)g(:)64 b Fe(The)26 b(classical)g(KAM)g(theory)g(at)h(the)g
(da)n(wn)f(of)h(the)g(t)n(w)n(en)n(t)n(y-\014rst)e(cen)n(tury)h(;)i
FC(Mosc)l(ow)i(Math.)287 4841 y(J.)d Fb(3)p Fe(\(3\),)h(p.)g(1113)d({)j
(1144)d(\(2003\))109 4988 y([25])48 b Fc(J.)27 b(Xu)h(and)g(J.)f(Y)-7
b(ou)28 b(:)65 b Fe(A)28 b(Note)f(on)h(the)g(pap)r(er)f(\\In)n(v)-5
b(arian)n(t)26 b(tori)h(for)g(nearly)g(in)n(tegrable)f(Hamiltonian)i
(systems)287 5087 y(with)g(degeneracy";)d(preprin)n(t,)i(Nanjing)h
(Univ)n(ersit)n(y)f(\(2006\))109 5234 y([26])48 b Fc(J.)22
b(Y)-7 b(ou)23 b(:)57 b Fe(A)24 b(KAM)e(Theorem)g(for)h(Hyp)r(erb)r
(olic-T)n(yp)r(e)f(Degenerate)g(Lo)n(w)n(er)f(Dimensional)h(T)-7
b(ori)22 b(in)h(Hamiltonian)287 5334 y(Systems)k(;)h
FC(Comm.)j(Math.)g(Phys.)e Fb(192)p Fe(\(1\),)e(p.)h(145)e({)h(168)f
(\(1998\))1950 5778 y FD(13)p eop end
%%Trailer

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