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1、CAMBRIDGESTUDIESINADVANCEDMATHEMATICS151EditialBoardB.BOLLOBASW.FULTONA.KATOKF.KIRWANP.SARNAKB.SIMONB.TOTAROFoundationsofErgodicTheyRichwithexamplesapplicationsthistextbookprovidesacoherentselfcontainedintroductiontoergo
2、dictheysuitablefavarietyofonetwosemestercourses.Theauths’clearfluentexpositionhelpsthereadertograspquicklythemostimptantideasofthetheytheiruseofconcreteexamplesillustratestheseideasputstheresultsintoperspective.Thebookre
3、quiresfewprerequisiteswithbackgroundmaterialsuppliedintheappendix.Thefirstfourchapterscoverelementarymaterialsuitablefundergraduatestudents–invariancerecurrenceergodicity–aswellassomeofthemainexamples.Theauthsthengradual
4、lybuilduptomesophisticatedtopicsincludingcrelationsequivalentsystemsentropythevariationalprinciplethermodynamicfmalism.The400exercisesincreaseindifficultythroughthetexttestthereader’sunderstingofthewholethey.Hintssolutio
5、nsareprovidedattheendofthebook.MarceloVianaisProfessofMathematicsatInstitutoNacionaldeMatematicaPuraeAplicada(IMPA)RiodeJaneiroaleadingresearchexpertinergodictheydynamicalsystems.Hehasservedinseveralacademicganizationssu
6、chastheInternationalMathematicalUnion(Vicepresident2011–2014)theBrazilianMathematicalSociety(President2013–2015)theLatinAmericanMathematicalUnion(ScientificCodinat2001–2008)thenewlyfoundedMathematicalCounciloftheAmericas
7、.HeisalsoamemberoftheacademiesofscienceofBrazilPtugalChiletheDevelopingWldhehasreceivedseveralacademicdistinctionsincludingtheGrCroixofScientificMeritgrantedbythePresidentofBrazilin2000theRamanujanPrizeofICTPIMUin2005.He
8、wasaninvitedspeakerattheinternationalcongressofmathematiciansICM1994inZurichaplenaryspeakerattheInternationalCongressofMathematicalPhysicsICMP1994aPlenarySpeakerattheICM1998inBerlin.Todatehehassupervised32doctaltheses.Cu
9、rrentlyheleadstheganizationoftheICM2018inRiodeJaneiroisalsoinvolvedininitiativestoimprovemathematicaleducationinhiscountry.KrerleyOliveiraisAssociateProfessattheUniversidadeFederaldeAlagoas(UFAL)Brazilwherehefoundedthegr
10、aduateprograminmathematicstheStateofAlagoasMathOlympiadprogramwherehepromotesyoungtalentsinmathematics.HewasamedalistattheBrazilianMathematicalOlympiad(1996)twiceattheIberoamericanMathematicalOlympiadfuniversitystudents(
11、19992000).HewaselectedanAffiliateMemberoftheBrazilianAcademyofSciences(2007–2012)hisresearchisfocusedondynamicalsystemsergodicthey.FoundationsofErgodicTheyMARCELOVIANAIMPARiodeJaneiroKRERLEYOLIVEIRAUniversidadeFederaldeA
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