遍歷性理論引論（影印版）

Chapter0
Preliminaries
0.1Introduction
0.2MeasureSpaces
0.3Integration
0.4AbsolutelyContinuousMeasuresandConditionalExpectations
0.5FunctionSpaces
0.6HaarMeasure
0.7CharacterTheory
0.8EndomorphismsofTori
0.9Perron-FrobeniusTheory
0.10Topology
Chapter1
Measure-PreservingTransformations
1.1DefinitionandExamples
1.2ProblemsinErgodicTheory
1.3AssociatedIsometries
1.4Recurrence
1.5Ergodicity
1.6TheErgodicTheorem
1.7Mixing
Chapter2
Isomorphism,Conjugacy,andSpectralIsomorphism
2.1PointMapsandSetMaps
2.2IsomorphismofMeasure-PreservingTransformations
2.3ConjugacyofMeasure-preservingTransformhtions
2.4TheIsomorphismProblem
2.5SpectralIsomorphism
2.6SpectralInvariants
Chapter3
Measure-PreservingTransformationswithDiscreteSpectrum
3.1EigenvaluesandEigenfunctions
3.2DiscreteSpectrum
3.3GroupRotations
Chapter4
Entropy
4.1PartitionsandSubalgebras
4.2EntropyofaPartition
4.3ConditionalEntropy
4.4EntropyofaMeasure-PreservingTransformation
4.5Propertiesorb(T,A)andh(T)
4.6SomeMethodsforCalculatingh(T)
4.7Examples
4.8HowGoodanInvariantisEntropy?
4.9BernoulliAutomorphismsandKolmogorovAutomorphisms
4.10ThePinsker-AlgebraofaMeasure-PreservingTransformation
4.11SequenceEntropy
4.12Non-invertibleTransformations
4.13Comments
Chapter5
TopologicalDynamics
5.1Examples
5.2Minimality
5.3TheNon-wanderingSet
5.4TopologicalTransitivity
5.5TopologicalConjugacyandDiscreteSpectrum
5.6ExpansiveHomeomorphisms
Chapter6
InvariantMeasuresforContinuousTransformations
6.1MeasuresonMetricSpaces
6.2InvariantMeasuresforContinuousTransformations
6.3InterpretationofErgodicityandMixing
6.4RelationofInvariantMeasurestoNon-wanderingSets,Periodic
PointsandTopologicalTransitivity
6.5UniqueErgodicity
6.6Examples
Chapter7
TopologicalEntropy
7.1DefinitionUsingOpenCovers
7.2Bowen'sDefinition
7.3CalculationofTopologicalEntropy
Chapter8
RelationshipBetweenTopologicalEntropyand
Measure-TheoreticEntropy
8.1TheEntropyMap
8.2TheVariationalPrinciple
8.3MeasureswithMaximalEntropy
8.4EntropyofAffineTransformations
8.5TheDistributionofPeriodicPoints
8.6DefinitionofMeasure-TheoreticEntropyUsingtheMetricsdn
Chapter9
TopologicalPressureandItsRelationshipwith
InvariantMeasures
9.1TopologicalPressure
9.2PropertiesofPressure
9.3TheVariationalPrinciple
9.4PressureDeterminesM(X,T)
9.5EquilibriumStates
Chapter10
ApplicationsandOtherTopics
10.1TheQualitativeBehaviourofDiffeomorphisms
10.2TheSubadditiveErgodicTheoremandtheMultiplicative
ErgodicTheorem
10.3Quasi-invariantMeasures
10.4OtherTypesofIsomorphism
10.5TransformationsofIntervals
10.6FurtherReading
References
Index