混沌动力系统的概念和结果

图书标准信息

• 作者 [法国]克莱（Collrt）、[瑞士]艾克曼（Eckmann J-P） 著
• 出版社 科学出版社
• 出版时间 2011-06
• 版次 1
• ISBN 9787030313898
• 定价 68.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 230页
• 字数 294千字
• 正文语种 英语
• 丛书 国外数学名著系列：73

【内容简介】

《混沌动力系统的概念和结果》介绍了混沌动力系统的概念和其拓扑性质、双曲率、不变测度、熵和其他概率结果。

【目录】

1ABasicProblem
2DynamicalSystems
2.1BasicsofMechanicalSystems
2.2FormalDefinitions
2.3Maps
2.4BasicExamplesofMaps
2.5MoreAdvancedExamples
2.6ExamplesofFlows

3TopologicalProperties
3.1Coding,Kneading
3.2TopologicalEntropy
3.2.1Topological,Measure,andMetricSpaces
3.2.2SomeExamples
3.2.3GeneralTheoryofTopologicalEntropy
3.2.4AMetricVersionofTopologicalEntropy
3.3Attractors

4Hyperbolicity
4.1HyperbolicFixedPoints
4.1.1StableandUnstableManifolds
4.1.2Conjugation
4.1.3Resonances
4.2InvariantManifolds
4.3NonwanderingPointsandAxiomASystems
4.4ShadowingandItsConsequences
4.4.1SensitiveDependenceonInitialConditions
4.4.2ComplicatedOrbitsOccurinHyperbolicSystems
4.4.3ChangeofMap
4.5ConstructionofMarkovPartitions

5InvariantMeasures
5.1Overview
5.2Details
5.3ThePerron-FrobeniusOperator
5.4TheErgodicTheorem
5.5ConvergenceRatesintheErgodicTheorem
5.6MixingandDecayofCorrelations
5.7PhysicalMeasures
5.8LyapunovExponents

6Entropy
6.1TheShannon-McMillan-BreimanTheorem
6.2Sinai-Bowen-RuelleMeasures
6.3Dimensions

7StatisticsandStatisticalMechanics
7.1TheCentralLimitTheorem
7.2LargeDeviations
7.3ExponentialEstimates
7.3.IConcentration
7.4TheFormalismofStatisticalMechanics
7.5MultifractalMeasures

8OtherProbabilisticResults
8.1EntranceandRecurrenceTimes
8.2NumberofVisitstoaSet
8.3Extremes
8.4Quasi-lnvariantMeasures
8.5StochasticPerturbations

9ExperimentalAspects
9.1CorrelationFunctionsandPowerSpectrum
9.2Resonances
9.3LyapunovExponents
9.4Reconstruction
9.5MeasuringtheLyapunovExponents
9.6MeasuringDimensions
9.7MeasuringEntropy
9.8EstimatingtheInvariantMeasure
References
Index