Partially Hyperbolic Dynamics

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1、ContentsPreface1Chapter1.Introduction31.1.Firstdefinitions31.2.Examples41.2.1.AnosovDiffeomorphisms41.2.2.AnosovFlows61.2.3.GeodesicFlows61.2.4.FrameFlows81.2.5.Affinediffeomorphisms91.2.6.LinearAutomorphismsonTori101.2.7.DirectProducts111.2.8.Fiberingsoverpartiallyhyperbolicdiffe

2、omorphisms.111.2.9.Skewproducts.12Chapter2.Stableergodicityofpartiallyhyperbolicdiffeomorphisms132.1.Introduction132.2.Pugh-ShubConjecture142.2.1.TheHopfargument152.2.2.TheHopfargumentforpartiallyhyperbolicdiffeomorphisms172.3.Accessibilityandaccessibilityclasses202.3.1.Proper

3、tiesoftheaccessibilityclasses202.4.AccessibilityisC1-open262.5.AccessibilityisC∞-dense282.5.1.TheKeepawayLemma292.5.2.TheUnweavingLemma322.5.3.Theconservativesetting34iiiivCONTENTS2.5.4.Thenon-conservativesetting372.6.Accessibilityimpliesergodicity382.6.1.Juliennes392.6.2.Pr

4、oofofTheorem2.6.3402.6.3.ProofofTheorem2.6.2452.7.ACriteriontoestablishergodicity482.7.1.PesinTheory482.7.2.ThePesinhomoclinicclasses502.7.3.Criterion512.7.4.Proof512.8.Stateoftheartin201157Chapter3.Partialhyperbolicityandentropy593.1.Introduction593.2.TheLedrappier-Walterse

5、ntropyformula613.3.IsotopictoAnosov643.3.1.Propertiesofthesemiconjugacy653.3.2.Uniquenessoftheentropymaximizingmeasure683.4.Compactcenterleaves683.4.1.NullcenterLyapunovexponent703.4.2.Non-vanishingcenterexponents743.4.3.Finitelymanymaximizingmeasures763.5.Miscellanyofresult

6、sonentropyandmaximizingmeasures783.5.1.h-expansivenessandmaximizingmeasures783.5.2.CenterLyapunovexponentofentropymaximizingmeasures793.5.3.TheEntropyConjecture81Chapter4.Partialhyperbolicityandcocycles854.1.Introduction854.2.Ergodicpropertiesofcocycles904.3.Accessibility904

7、.4.Holonomyinvarianceandcontinuityofconditionalmeasures944.5.Absolutecontinuityofcenterfoliationsandrigidity994.5.1.Conservativesystems994.5.2.Dissipativesystems101CONTENTSvChapter5.Partialhyperbolicityindimension31035.1.Introduction1035.2.Preliminaries1085.2.1.Geometricprel

8、iminaries1085.2.2.Topologicpreliminaries1105.2.3.Dynamicpreliminaries1125.3