遍历性理论引论

图书标准信息

• 作者 P.Walters 编
• 出版社 世界图书出版公司
• 出版时间 2003-06
• 版次 1
• ISBN 9787506260091
• 定价 28.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 250页
• 字数 11千字

【内容简介】

In1970IgaveagraduatecourseinergodictheoryattheUniversityofMarylandinCollegePark,andtheselectureswerethebasisoftheSpringerLectureNotesinMathematicsVolume458called"ErgodicTheory--IntroductoryLectures"whichwaspublishedin1975.Thisvolumeisnowoutofprint,soIdecidedtoreviseandaddtothecontentsofthesenotes.Ihaveupdatedtheearlierchaptersandhaveaddedsomenewchaptersontheergodictheoryofcontinuoustransformationsofcompactmetricspaces.Inparticular,Ihaveincludedsomematerialontopologicalpressureandequilibriumstates.Inrecentyearstherehavebeensomefascinatinginteractionsofergodictheorywithdifferentiabledynamics,differentialgeometry,numbertheory,vonNeumannalgebras,probabilitytheory,statisticalmechanics,andothertopics.InChapter101havebrieflydescribedsomeoftheseandgivenreferencestosomeoftheothers.Ihopethatthisbookwillgivethereaderenoughfoundationtotackletheresearchpapersonergodictheoryanditsapplications.

【目录】

Chapter0Preliminaries
0.1Introduction
0.2MeasureSpaces
0.3Integration
0.4AbsolutelyContinuousMeasuresandConditionalExpectations
0.5FunctionSpaces
0.6HaarMeasure
0.7CharacterTheory
0.8EndomorphismsofTori
0.9Perron-FrobeniusTheory
0.10Topology

Chapter1Measure-PreservingTransformations
1.1DefinitionandExamples
1.2ProblemsinErgodicTheory
1.3AssociatedIsometries
1.4Recurrence
1.5Ergodicity
1.6TheErgodicTheorem
1.7Mixing

Chapter2Isomorphism,Conjugacy,andSpectralIsomorphism
2.1PointMapsandSetMaps
2.2IsomorphismofMeasure-PreservingTransformations
2.3ConjugacyofMeasure-preservingTransformhtions
2.4TheIsomorphismProblem
2.5SpectralIsomorphism
2.6SpectralInvariants

Chapter3Measure-PreservingTransformationswithDiscreteSpectrum
3.1EigenvaluesandEigenfunctions
3.2DiscreteSpectrum
3.3GroupRotations

Chapter4Entropy
4.1PartitionsandSubalgebras
4.2EntropyofaPartition
4.3ConditionalEntropy
4.4EntropyofaMeasure-PreservingTransformation
4.5PropertiesorbT,AandhT
4.6SomeMethodsforCalculatinghT
4.7Examples
4.8HowGoodanInvariantisEntropy
4.9BernoulliAutomorphismsandKolmogorovAutomorphisms
4.10ThePinsker-AlgebraofaMeasure-PreservingTransformation
4.11SequenceEntropy
4.12Non-invertibleTransformations
4.13Comments

Chapter5TopologicalDynamics
5.1Examples
5.2Minimality
5.3TheNon-wanderingSet
5.4TopologicalTransitivity
5.5TopologicalConjugacyandDiscreteSpectrum
5.6ExpansiveHomeomorphisms

Chapter6InvariantMeasuresforContinuousTransformations
6.1MeasuresonMetricSpaces
6.2InvariantMeasuresforContinuousTransformations
6.3InterpretationofErgodicityandMixing
6.4RelationofInvariantMeasurestoNon-wanderingSets,PeriodicPointsandTopologicalTransitivity
6.5UniqueErgodicity
6.6Examples

Chapter7TopologicalEntropy
7.1DefinitionUsingOpenCovers
7.2Bowen'sDefinition
7.3CalculationofTopologicalEntropy

Chapter8RelationshipBetweenTopologicalEntropyandMeasure-TheoreticEntropy
8.1TheEntropyMap
8.2TheVariationalPrinciple
8.3MeasureswithMaximalEntropy
8.4EntropyofAffineTransformations
8.5TheDistributionofPeriodicPoints
8.6DefinitionofMeasure-TheoreticEntropyUsingtheMetricsdn

Chapter9TopologicalPressureandItsRelationshipwithInvariantMeasures
9.1TopologicalPressure
9.2PropertiesofPressure
9.3TheVariationalPrinciple
9.4PressureDeterminesMX,T
9.5EquilibriumStates

Chapter10ApplicationsandOtherTopics
10.1TheQualitativeBehaviourofDiffeomorphisms
10.2TheSubadditiveErgodicTheoremandtheMultiplicativeErgodicTheorem
10.3Quasi-invariantMeasures
10.4OtherTypesofIsomorphism
10.5TransformationsofIntervals
10.6FurtherReading
References
Index