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1、TheTopologyofChaosAliceinStretchandSqueezelandRobertGilmoreMarcLefrancWILEY-INTERSCIENCEAJOHNWILEY&SONS,INC.,PUBLICATIONThispageisintentionallyleftblankTheTopologyofChaosThispageisintentionallyleftblankTheTopologyofChaosAliceinStretchandSqueezelandRobertGilmoreMarcLefrancWILEY-
2、INTERSCIENCEAJOHNWILEY&SONS,INC.,PUBLICATIONlhistextisprintedonacid-freepaper.@Copyrightmi;!2002byJohnWiley&Sons.Inc..NewYork.AllrightsreservedI’uhlislicdsimuIlancouslyinC;inaclaNopartofthispublicationmaybereproduced,storcdinaretrievalsystemortraiisinittedinanyfoiiiiorbyanymean
3、s,electronic.mechanical.photocopyilig.recording.scanningorotherwise,exceptaspermittedundcrSection107or108ofthclY76UnitcdStatesCopyrightAct.withouteitherthepriorwrittenpermissionofthePublisher.orauthorizationthroughpaymentoftlieappropriatcper-copyfeetotheCopyright(‘lcaranccC‘cnt
4、cr.222RosewoodDrivc.Daiivcrs,MA01923,(978)750-8400.fax(978)750-4744,RequcslstotlicPublisllcrforpermissionsl~ouldbeaddressedtothePermissionsDepartment.JohnWiley&Sons.Inc.,605ThirdAvenue,NewYork,NY101~8-0012,(2121X~O-h011.fax(212)X50-6008.E-Mail:PEKMREQidWILF,Y.COM.Fororderingand
5、customerseie.call1-800-CALL-WILEYLibrut-vuJ’CungrcwCu1ulo~ing-in-Piiblic.a~iurrDUIU1.rAvuilublcISBN0-471-408I(1-hPrintedintheUnitedStatesofAmerica10987654321PrefaceBeforethe1970sopportunitiessometimesaroseforphysiciststostudynonlinearsystems.Thiswasespeciallytrueinfieldslikeflu
6、iddynamicsandplasmaphysics,wherethehndamentalequationsarenonlinearandthesenonlinearitiesmasked(andstillmask)thefullspectrumofspectacularlyrichbehavior.Whenpossibleweavoidedbeingdraggedintothestudyofabstractnonlinearsystems.Forwebelieved,toparaphraseabeautifulgeneralizationofTol
7、stoy,thatAlllinearsystemsarethesame.Eachnonlinearsystemisnonlinearinitsownway.Atthattimewebelievedthatonecouldspendawholelifetimestudyingthenonlinear-itiesofthevanderPoloscillator[CartwrightandLittlewood(1949,Levinson(1949)]andwindupknowingnexttonothingaboutthebehavioroftheDuff
8、ingoscillator.Nevertheless,otherintrepidresearchershad
