graph directed markov systems (mauldin r d,urbanski m)

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1、ThispageintentionallyleftblankCAMBRIDGETRACTSINMATHEMATICSGeneralEditorsB.BOLLOBAS,W.FULTON,A.KATOK,F.KIRWAN,P.SARNAK148GraphDirectedMarkovSystemsR.DanielMauldinandMariuszUrba´nskiGraphDirectedMarkovSystemsGeometryanddynamicsoflimitsetsCamb

2、ridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,SãoPauloCambridgeUniversityPressTheEdinburghBuilding,Cambridge,UnitedKingdomPublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYorkwww.cambridge.orgInformationonthistitle:www.cambridge.org/97805

3、21825382©CambridgeUniversityPress2003Thisbookisincopyright.Subjecttostatutoryexceptionandtotheprovisionofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpublishedinprintformat2003

4、-isbn-13978-0-511-07091-4eBook(EBL)-isbn-100-511-07091-8eBook(EBL)-isbn-13978-0-521-82538-2hardback-isbn-100-521-82538-5hardbackCambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyofsforexternalorthird-partyinternetw

5、ebsitesreferredtointhisbook,anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,accurateorappropriate.ContentsIntroductionpagevii1Preliminaries12SymbolicDynamics42.1Topologicalpressureandvariationalprinciples52.2Gibbsstates,equilibriumstatesandpotential

6、s122.3Perron–Frobeniusoperator262.4Ionescu-TulceaandMarinescuinequality312.5Stochasticlaws402.6AnalyticpropertiesofpressureandthePerron–Frobeniusoperator432.7TheexistenceofeigenmeasuresoftheConjugatePerron–FrobeniusoperatorandofGibbsstates483H¨olderFamiliesofFunct

7、ionsandF-ConformalMeasures543.1SummableH¨olderfamilies543.2F-conformalmeasures574ConformalGraphDirectedMarkovSystems624.1SomepropertiesofconformalmapsinRdwithd≥2624.2Conformalmeasures;Hausdorffandboxdimensions714.3Stronglyregular,hereditarilyregularandirregularsyst

8、ems874.4Dimensionsofmeasures904.5Hausdorff,packingandLebesguemeasures944.6Porosityoflimitsets1034.7Theassociatediteratedfunctionsystem1074.8Refinedgeometr