Content-Type: multipart/mixed; boundary="-------------0604031538805" This is a multi-part message in MIME format. ---------------0604031538805 Content-Type: text/plain; name="06-106.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="06-106.keywords" Hard balls, Bolzmann-Sinai hypothesis, semi-dispersing billiards, ergodicity, Lyapunov function ---------------0604031538805 Content-Type: application/postscript; name="Qgrow.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="Qgrow.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.94b Copyright 2004 Radical Eye Software %%Title: Qgrow.dvi %%CreationDate: Mon Apr 03 15:26:55 2006 %%Pages: 12 %%PageOrder: Ascend %%BoundingBox: 0 0 595 842 %%DocumentFonts: CMR17 CMR12 CMR10 CMBX10 CMMI10 CMBX12 CMMI12 CMSY10 %%+ CMMI8 CMR7 CMSY8 CMTI12 CMR8 MSBM10 CMCSC10 CMMI6 CMR6 CMEX10 CMSY6 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips.exe Qgrow.dvi %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2006.04.03:1526 %%BeginProcSet: tex.pro 0 0 %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S /BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: psfrag.pro 0 0 %% %% This is file `psfrag.pro', %% generated with the docstrip utility. %% %% The original source files were: %% %% psfrag.dtx (with options: `filepro') %% %% Copyright (c) 1996 Craig Barratt, Michael C. 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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: 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 10 /angbracketleftbig put dup 11 /angbracketrightbig put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 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 48 /zero put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 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 115 /s put dup 116 /t put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 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 82 /R put dup 97 /a put dup 101 /e put dup 107 /k put dup 109 /m put dup 114 /r put readonly def /FontBBox{14 -250 1077 750}readonly def /UniqueID 5000772 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 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: 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 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 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 12 /fi put dup 13 /fl put dup 34 /quotedblright 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 50 /two put dup 51 /three put dup 53 /five 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 75 /K put dup 76 /L put dup 77 /M put dup 79 /O put dup 80 /P put dup 83 /S put dup 84 /T put dup 87 /W put dup 92 /quotedblleft put dup 96 /quoteleft 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 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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 3 /asteriskmath put dup 63 /perpendicular put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D5FC1B2109839E5B52DFBB2A7C1B5D8E7E8AA0 5B10EA43D6A8ED61AF5B23D49920D8F79DAB6A59062134D84AC0100187A6CD1F 80F5DDD9D222ACB1C23326A7656A635C4A241CCD32CBFDF8363206B8AA36E107 1477F5496111E055C7491002AFF272E46ECC46422F0380D093284870022523FB DA1716CC4F2E2CCAD5F173FCBE6EDDB874AD255CD5E5C0F86214393FCB5F5C20 9C3C2BB5886E36FC3CCC21483C3AC193485A46E9D22BD7201894E4D45ADD9BF1 CC5CF6A5010B5654AC0BE0DA903DB563B13840BA3015F72E51E3BC80156388BA F83C7D393392BCBC227771CDCB976E933025375FFCDD9E2FD073678A57A333F9 6BDA68191ED103DB904FC6A75017A9939B1F14A711BC0B140F6C4E6C217EEADC 2B649171318049FC272C351B1417B517204D5DBE34FA6D6B93E1E6086F880CF6 401E7F67B5A91AD4822EF52F13060CBCF81FCA8120CD5D8360F7D2C81EC04625 72F94F9676DE469FB36857FD8683430A234CE2DDA9FB813F2A4BA76FED8025B4 94499FE3316EA5B81AF1664D5C38FB727E469D20E48EA4E7414B7A5FAD4FCD36 1BA213E004FF647E1ECD343BA1B878BF06B93F7A2EEC08BDB0FBFCCFCAE858BE EC8D196DEA158F6C2C5CFABF54BC74ABA6E68F1A8B8375FCEE77FB120977DF2B B551AAC2A1BE3CE4F7997827779418104F0687F9230283B2A6529C861F5CDD3E 5D361F561E3BB620E59469FB7D390DB1372B55006FADB2BF3290971211E081CB 9050CE314E86EECF24EFD447FCB51573BEB0B06A6D59365957CC7427BBA8AC51 04B50368ED9F1E5DE47A5780E16F4AA0ED76022F76E09F9DCEEA7FC63B28BE9B D0F4566D2C5EEF993EC9F9F8943025C614054EC86F8408A17C68D39C8B4BDBEB 4CE7AEB796A9475FF45FD41A3502A00C7FAAF7BC0FEE9820D25908FFAC81E251 6097425177DA64F9DB84A0D9C2B2AD844F8A74CDAA552CBEBCE5507BC028A2EE 8B60557B0B03DF22FEA1E0A27F261D277C2E579E227224F9FA7D978B452BACD9 5E19823AAE79782C1E1CABE936B7820AF1 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 49 /one put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 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 61 /slash put dup 78 /N put dup 100 /d put dup 105 /i put dup 113 /q 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: 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 20 /lessequal put dup 21 /greaterequal put dup 26 /propersubset put dup 33 /arrowright put dup 50 /element put dup 54 /negationslash put dup 56 /universal put dup 68 /D put dup 75 /K put dup 84 /T put dup 91 /union put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 110 /backslash put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 14 /delta put dup 21 /lambda put dup 22 /mu put dup 23 /nu put dup 30 /phi put dup 34 /epsilon put dup 39 /phi1 put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 67 /C put dup 68 /D put dup 74 /J put dup 78 /N put dup 81 /Q put dup 82 /R put dup 83 /S put dup 85 /U put dup 86 /V put dup 99 /c put dup 100 /d put dup 105 /i put dup 109 /m put dup 110 /n put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-30 -250 1026 750}readonly def /UniqueID 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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 8 /Phi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 19 /acute put dup 34 /quotedblright put dup 38 /ampersand 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 87 /W put dup 89 /Y put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 96 /quoteleft 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 readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 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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 74 /J 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 13 /fl 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 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 64 /at put dup 65 /A put dup 66 /B put dup 68 /D put dup 69 /E put dup 70 /F put dup 76 /L put dup 77 /M put dup 79 /O put dup 80 /P put dup 83 /S put dup 84 /T put dup 85 /U 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 106 /j put 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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%!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 45 /hyphen put dup 70 /F 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 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 121 /y put readonly def /FontBBox{-33 -250 945 749}readonly def /UniqueID 5000795 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 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Fp(0)p Fi(,)35 b(then)g(for)f(al)5 b(l)35 b Fn(t)28 b Fm(\025)g Fp(0)1410 3770 y Fm(k)p Fn(w)1530 3785 y Fl(t)1559 3770 y Fm(k)f(\025)i(k)p Fn(w)1862 3785 y Fh(0)1901 3770 y Fm(k)22 b Fp(+)2081 3702 y Fm(j)p Fn(Q)p Fp(\()p Fn(n)2282 3717 y Fh(0)2321 3702 y Fp(\))p Fm(j)17 b Fn(t)p 2081 3747 358 4 v 2155 3838 a Fm(k)p Fn(w)2275 3853 y Fh(0)2314 3838 y Fm(k)2449 3770 y Fn(:)324 4013 y Fi(Pr)-5 b(o)g(of.)48 b Fp(F)-8 b(or)32 b(an)m(y)h Fn(t)28 b(>)g Fp(0,)k(whic)m(h)i(is)f(not) g(a)f(collision)h(time,)605 4189 y Fn(d)p 587 4233 86 4 v 587 4324 a(dt)683 4256 y Fm(k)p Fn(w)803 4271 y Fl(t)832 4256 y Fm(k)882 4215 y Fh(2)949 4256 y Fp(=)1080 4189 y Fn(d)p 1063 4233 V 1063 4324 a(dt)1159 4256 y Fm(h)p Fn(w)1268 4271 y Fl(t)1297 4256 y Fn(;)g(w)1427 4271 y Fl(t)1456 4256 y Fm(i)28 b Fp(=)f Fm(\000)p Fp(2)p Fm(h)p Fn(z)1836 4271 y Fl(t)1866 4256 y Fn(;)34 b(w)1997 4271 y Fl(t)2026 4256 y Fm(i)27 b Fp(=)h(2)p Fm(j)p Fn(Q)p Fp(\()p Fn(n)2446 4271 y Fl(t)2476 4256 y Fp(\))p Fm(j)f(\025)2684 4189 y Fp(2)17 b Fm(j)p Fn(Q)p Fp(\()p Fn(n)2951 4204 y Fh(0)2990 4189 y Fp(\))p Fm(j)g(k)p Fn(w)3193 4204 y Fl(t)3221 4189 y Fm(k)p 2684 4233 588 4 v 2873 4324 a(k)p Fn(w)2993 4339 y Fh(0)3032 4324 y Fm(k)3281 4256 y Fn(;)324 4505 y Fp(where)34 b(w)m(e)f(used)h(\(2.2\))e(and)h(the)g (previous)h(prop)s(osition,)e(hence)1575 4686 y Fn(d)p 1557 4730 86 4 v 1557 4821 a(dt)1653 4753 y Fm(k)p Fn(w)1773 4768 y Fl(t)1802 4753 y Fm(k)c(\025)1995 4686 y(j)p Fn(Q)p Fp(\()p Fn(n)2196 4701 y Fh(0)2235 4686 y Fp(\))p Fm(j)p 1995 4730 307 4 v 2044 4821 a(k)p Fn(w)2164 4836 y Fh(0)2203 4821 y Fm(k)2311 4753 y Fn(:)324 5002 y Fp(Since)33 b Fm(k)p Fn(w)698 5017 y Fl(t)728 5002 y Fm(k)f Fp(do)s(es)h(not)f(c)m (hange)i(at)e(collisions,)i(the)f(prop)s(osition)g(follo)m(ws.)p 3491 5002 4 66 v 3495 4940 59 4 v 3495 5002 V 3553 5002 4 66 v 1918 5251 a(9)p eop end %%Page: 10 10 TeXDict begin 10 9 bop 470 548 a Fp(Next)32 b(w)m(e)f(assume)i(that)d Fn(Q)p Fp(\()p Fn(t)p Fp(\))e Fn(<)g Fp(0)i(on)h(all)g(of)f(the)h (manifold)g Fn(J)9 b Fp(;)31 b(more)g(sp)s(eci\014cally)324 768 y(\(2.5\))825 b Fn(Q)p Fp(\()p Fn(n)1523 783 y Fh(0)1563 768 y Fp(\))27 b(=)h Fm(h)p Fn(z)1816 783 y Fh(0)1855 768 y Fn(;)34 b(w)1986 783 y Fh(0)2025 768 y Fm(i)27 b(\024)i(\000)p Fn(c)2316 783 y Fh(0)2383 768 y Fn(<)f Fp(0)324 988 y(holds)40 b(true)g(uniformly)g(across)h Fn(J)49 b Fp(for)39 b(a)g(unit)h(normal)f(v)m(ector)i(\014eld)g Fn(n)3020 1003 y Fh(0)3059 988 y Fp(\()p Fn(y)t Fp(\))e(\()p Fn(y)k Fm(2)d Fn(J)9 b Fp(\))324 1108 y(with)33 b(a)f(\014xed)i (constan)m(t)f Fn(c)1298 1123 y Fh(0)1366 1108 y Fn(>)27 b Fp(0.)324 1312 y Fa(Theorem)i(2.6.)35 b Fi(If)27 b(\(2.5\))g(holds,)h (then)f Fp(\010)1883 1276 y Fl(t)1940 1312 y Fi(exp)-5 b(ands)26 b(the)i(volume)f(of)g(the)g(hyp)-5 b(ersurfac)g(e)324 1432 y Fn(J)44 b Fi(at)35 b(any)g(p)-5 b(oint)34 b Fn(y)d Fm(2)d Fn(J)44 b Fi(by)35 b(a)g(factor)g Fn(\025)1795 1447 y Fl(t)1852 1432 y Fm(\025)28 b Fp(1)22 b(+)g Fn(c)2168 1447 y Fh(0)2207 1432 y Fn(t)35 b Fi(for)g(al)5 b(l)35 b Fn(t)27 b Fm(\025)i Fp(1)p Fn(=c)2881 1447 y Fh(0)2920 1432 y Fi(.)324 1636 y(Pr)-5 b(o)g(of.)48 b Fp(Com)m(bining)34 b(Prop)s(ositions)f(2.2)g(and)f(2.5)g(giv)m(es)1215 1892 y Fn(\025)1272 1907 y Fl(t)1330 1892 y Fp(=)27 b Fm(k)p Fn(n)1541 1907 y Fl(t)1571 1892 y Fm(k)g(\025)h(k)p Fn(w)1873 1907 y Fl(t)1903 1892 y Fm(k)f(\025)h(k)p Fn(w)2205 1907 y Fh(0)2244 1892 y Fm(k)22 b Fp(+)2470 1824 y Fn(c)2512 1839 y Fh(0)2552 1824 y Fn(t)p 2424 1869 209 4 v 2424 1960 a Fm(k)p Fn(w)2544 1975 y Fh(0)2583 1960 y Fm(k)2643 1892 y Fn(:)324 2167 y Fp(Since)33 b Fm(k)p Fn(w)698 2182 y Fh(0)737 2167 y Fm(k)28 b(\024)g(k)p Fn(n)1028 2182 y Fh(0)1068 2167 y Fm(k)f Fp(=)h(1,)k(this)h(lo)m(w)m(er)h(b)s (ound)e(is)h(at)f(least)i(1)21 b(+)h Fn(c)2758 2182 y Fh(0)2797 2167 y Fn(t)33 b Fp(for)f Fn(t)c Fm(\025)g Fp(1)p Fn(=c)3322 2182 y Fh(0)3361 2167 y Fp(.)p 3491 2167 4 66 v 3495 2105 59 4 v 3495 2167 V 3553 2167 4 66 v 470 2363 a Fa(Ac)m(kno)m(wledgemen)m(t)p Fp(.)43 b(N.)29 b(C.)g(w)m(as)g(partially)g(supp)s(orted)h(b)m(y)f(NSF)g(gran)m (t)f(DMS-)324 2483 y(0354775.)42 b(N.)32 b(S.)h(w)m(as)h(partially)f (supp)s(orted)g(b)m(y)h(NSF)e(gran)m(t)h(DMS-0457168.)324 2816 y Fo(References)324 3035 y Fp([BCST02])49 b(P)-8 b(.)25 b(Balin)m(t,)i(N.)e(Cherno)m(v,)j(D.)c(Szasz,)k(and)c(I.)h(P)-8 b(.)25 b(T)-8 b(oth,)27 b Fi(Multi-dimensional)788 3155 y(semi-disp)-5 b(ersing)35 b(bil)5 b(liar)-5 b(ds:)48 b(singularities)37 b(and)f(the)h(fundamental)f(the)-5 b(o-)788 3275 y(r)g(em)p Fp(,)33 b(Ann.)g(H.)g(P)m(oincar)m(\023)-46 b(e)33 b Fa(3)g Fp(\(2002\),)e(451{482.)324 3479 y([BCST03])49 b(P)-8 b(.)48 b(Balin)m(t,)j(N.)c(Cherno)m(v,)52 b(D.)47 b(Szasz,)52 b(and)47 b(I.)g(P)-8 b(.)48 b(T)-8 b(oth,)50 b Fi(Ge)-5 b(ometry)49 b(of)788 3599 y(multidimensional)29 b(disp)-5 b(ersing)30 b(bil)5 b(liars)p Fp(,)28 b(Ast)m(\023)-46 b(erisque,)31 b Fa(286)d Fp(\(2003\),)g(119{)788 3720 y(150.)324 3923 y([Ch94])188 b(N.)25 b(Cherno)m(v,)j Fi(Statistic)-5 b(al)28 b(pr)-5 b(op)g(erties)27 b(of)g(the)h(p)-5 b(erio)g(dic)27 b(L)-5 b(or)g(entz)27 b(gas.)g(Mul-)788 4043 y(tidimensional)34 b(c)-5 b(ase)p Fp(,)32 b(J.)g(Stat.)h(Ph)m(ys.) h Fa(74)f Fp(\(1994\),)e(11{53.)324 4247 y([KB94])167 b(A.)31 b(Katok)f(and)g(K.)g(Burns)h Fi(In\014nitesimal)g(Lyapunov)i (functions,)f(invari-)788 4367 y(ant)43 b(c)-5 b(one)42 b(families)f(and)h(sto)-5 b(chastic)42 b(pr)-5 b(op)g(erties)42 b(of)g(smo)-5 b(oth)42 b(dynamic)-5 b(al)788 4488 y(systems)p Fp(,)33 b(Ergo)s(d.)f(Th.)i(Dyn.)e(Syst.)i Fa(14)f Fp(\(1994\),)e (757{785.)324 4691 y([KSS90])128 b(A.)36 b(Kr\023)-49 b(amli,)35 b(N.)h(Sim\023)-49 b(an)m(yi)36 b(&)f(D.)f(Sz\023)-49 b(asz,)37 b Fi(A)h(\\tr)-5 b(ansversal")36 b(fundamental)788 4811 y(the)-5 b(or)g(em)45 b(for)f(semi-disp)-5 b(ersing)43 b(bil)5 b(liar)-5 b(ds)p Fp(,)45 b(Comm.)f(Math.)g(Ph)m(ys.,)k Fa(129)788 4932 y Fp(\(1990\),)32 b(535{560)1894 5251 y(10)p eop end %%Page: 11 11 TeXDict begin 11 10 bop 324 548 a Fp([KSS91])128 b(A.)31 b(Kr\023)-49 b(amli,)31 b(N.)f(Sim\023)-49 b(an)m(yi)32 b(&)e(D.)g(Sz\023)-49 b(asz,)32 b Fi(The)g(K{Pr)-5 b(op)g(erty)33 b(of)f(Thr)-5 b(e)g(e)32 b(Bil-)788 668 y(liar)-5 b(d)35 b(Bal)5 b(ls)p Fp(,)32 b(Ann.)h(Math.,)g Fa(133)f Fp(\(1991\),)g(37{72) 324 872 y([KSS92])128 b(A.)27 b(Kr\023)-49 b(amli,)28 b(N.)f(Sim\023)-49 b(an)m(yi)28 b(&)e(D.)g(Sz\023)-49 b(asz,)29 b Fi(The)g(K-pr)-5 b(op)g(erty)29 b(of)g(four)g(bil)5 b(liar)-5 b(d)788 992 y(b)g(al)5 b(ls)p Fp(,)32 b(Comm.)i(Math.)f(Ph)m (ys.)h Fa(144)f Fp(\(1992\),)e(107{142.)324 1196 y([L)-11 b(W95])162 b(C.)41 b(Liv)m(erani)h(and)e(M.)h(W)-8 b(o)5 b(jtk)m(o)m(wski,)45 b Fi(Er)-5 b(go)g(dicity)42 b(in)g(Hamiltonian)f (sys-)788 1316 y(tems)p Fp(,)i(Dynamics)f(rep)s(orted,)h(Dynam.)e(Rep)s (ort.)g(Exp)s(ositions)h(Dynam.)788 1436 y(Systems)35 b(\(N.S.\))e Fa(4)p Fp(,)g(Springer,)g(Berlin)g(\(1995\),)f(130{202.) 324 1640 y([Sim92a])101 b(N.)39 b(Sim\023)-49 b(an)m(yi,)40 b Fi(The)g(K-pr)-5 b(op)g(erty)39 b(of)h Fn(N)50 b Fi(bil)5 b(liar)-5 b(d)39 b(b)-5 b(al)5 b(ls)39 b(I)p Fp(,)f(In)m(v)m(en)m(t.)i (Math.,)788 1760 y Fa(108)33 b Fp(\(1992\),)f(521{548.)324 1963 y([Sim92b])96 b(N.)38 b(Sim\023)-49 b(an)m(yi,)39 b Fi(The)f(K-pr)-5 b(op)g(erty)39 b(of)g Fn(N)49 b Fi(bil)5 b(liar)-5 b(d)38 b(b)-5 b(al)5 b(ls)38 b(II)p Fp(,)e(In)m(v)m(en)m(t.)j (Math.)788 2084 y Fa(110)33 b Fp(\(1992\),)f(151{172.)324 2287 y([SS99])204 b(N.)39 b(Sim\023)-49 b(an)m(yi)39 b(&)f(D.)f(Sz\023)-49 b(asz,)41 b Fi(Har)-5 b(d)40 b(b)-5 b(al)5 b(l)39 b(systems)h(ar)-5 b(e)40 b(c)-5 b(ompletely)39 b(hyp)-5 b(er-)788 2408 y(b)g(olic)p Fp(,)32 b(Ann.)i(Math.)e Fa(149)h Fp(\(1999\),)f(35{96.)324 2611 y([Sim02])150 b(N.)33 b(Sim\023)-49 b(an)m(yi,)34 b Fi(The)g(Complete)g(hyp)-5 b(erb)g(olicity)35 b(of)f(cylindric)g(bil)5 b(liar)-5 b(ds)p Fp(,)32 b(Er-)788 2731 y(go)s(d.)h(Th.)g(Dynam.)g(Syst.)g Fa(22)g Fp(\(2002\),)f(281{302.)324 2935 y([Sim03])150 b(N.)43 b(Sim\023)-49 b(an)m(yi)43 b Fi(Pr)-5 b(o)g(of)43 b(of)g(the)h(Boltzmann-Sinai)d(er)-5 b(go)g(dic)43 b(hyp)-5 b(othesis)43 b(for)788 3055 y(typic)-5 b(al)35 b(har)-5 b(d)35 b(disk)f(systems)p Fp(,)e(In)m(v)m(en)m(t.)j(Math.)e Fa(154)g Fp(\(2003\),)e(123{178.)324 3259 y([Sim04])150 b(N.)45 b(Sim\023)-49 b(an)m(yi)45 b Fi(Pr)-5 b(o)g(of)45 b(of)g(the)g(er)-5 b(go)g(dic)44 b(hyp)-5 b(othesis)45 b(for)g(typic)-5 b(al)45 b(har)-5 b(d)45 b(b)-5 b(al)5 b(l)788 3379 y(systems)p Fp(,)33 b(Ann.)g(H.)g(P)m(oincar)m(\023)-46 b(e)33 b Fa(5)g Fp(\(2004\),)f(203{233.)324 3582 y([Sin63])177 b(Y)-8 b(a.)45 b(G.)f(Sinai,)k Fi(On)e(the)g(F)-7 b(oundation)45 b(of)g(the)h(Er)-5 b(go)g(dic)46 b(Hyp)-5 b(othesis)46 b(for)788 3703 y(a)39 b(Dynamic)-5 b(al)38 b(System)g(of)h(Statistic)-5 b(al)38 b(Me)-5 b(chanics)p Fp(,)37 b(Dokl.)g(Ak)-5 b(ad.)37 b(Nauk)788 3823 y(SSSR,)c Fa(153)g Fp(\(1963\),)f(1261{1264.)324 4027 y([Sin70])177 b(Y)-8 b(a.)36 b(G.)g(Sinai,)h Fi(Dynamic)-5 b(al)36 b(systems)i(with)f(elastic)h(r)-5 b(e\015e)g(ctions.)37 b(Er)-5 b(go)g(dic)788 4147 y(pr)g(op)g(erties)47 b(of)g(disp)-5 b(ersing)46 b(bil)5 b(liar)-5 b(ds)p Fp(,)49 b(Russ.)e(Math.)f(Surv.)h Fa(25)g Fp(\(1970\),)788 4267 y(137{189.)324 4471 y([Sin79])177 b(Y)-8 b(a.)68 b(G.)g(Sinai,)77 b Fi(Development)66 b(of)h(Krylov's)g (ide)-5 b(as)p Fp(,)76 b(Afterw)m(ord)69 b(to)788 4591 y(N.)52 b(S.)f(Krylo)m(v,)56 b Fi(Works)c(on)f(the)h(foundations)f(of)g (statistic)-5 b(al)52 b(physics)p Fp(.)788 4711 y(Princeton)34 b(U.)f(Press,)h(Princeton,)g(N.)f(J.)f(\(1979\),)g(239{281.)1894 5251 y(11)p eop end %%Page: 12 12 TeXDict begin 12 11 bop 324 548 a Fp([SC82])188 b(Y)-8 b(a.)33 b(G.)g(Sinai)g(and)g(N.)g(I.)h(Cherno)m(v,)g Fi(Entr)-5 b(opy)36 b(of)f(a)g(gas)g(of)g(har)-5 b(d)35 b(spher)-5 b(es)788 668 y(with)41 b(r)-5 b(esp)g(e)g(ct)40 b(to)h(the)g(gr)-5 b(oup)40 b(of)h(sp)-5 b(ac)g(e-time)39 b(tr)-5 b(anslations)p Fp(,)40 b(T)-8 b(rudy)40 b(Sem.)788 789 y(P)m(etro)m(vsk)m(ogo,)i Fa(8)c Fp(\(1982\))f(218{238)g(\(in)h (Russian\),)j(and)d(in:)55 b(Dynamical)788 909 y(Systems,)e(Ed.)48 b(b)m(y)g(Y)-8 b(a.)47 b(Sinai,)k(Adv.)c(Series)i(in)e(Nonlin.)h (Dynam.,)j Fa(1)p Fp(,)788 1029 y(373{390)31 b(\(in)i(English\).)324 1233 y([SC85])188 b(Y)-8 b(a.)34 b(G.)g(Sinai)g(and)g(N.)g(I.)g(Cherno) m(v,)h(unpublished)i(man)m(uscript,)e(a)f(draft)788 1353 y(v)m(ersion)h(of)d([SC87].)324 1557 y([SC87])188 b(Y)-8 b(a.)23 b(G.)g(Sinai)g(and)g(N.)g(I.)g(Cherno)m(v,)j Fi(Er)-5 b(go)g(dic)26 b(pr)-5 b(op)g(erties)25 b(of)h(some)f(systems) 788 1677 y(of)47 b(2-dimensional)e(discs)h(and)h(3-dimensional)d(spher) -5 b(es)p Fp(,)49 b(Russ.)d(Math.)788 1797 y(Surv.)34 b Fa(42)f Fp(\(1987\),)e(181{207.)1894 5251 y(12)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF ---------------0604031538805--