确定性系统的统计性质

图书标准信息

• 作者 丁玖、周爱辉 编
• 出版社 清华大学出版社
• 出版时间 2008-11
• 版次 1
• ISBN 9787302182962
• 定价 48.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 236页
• 字数 355千字

【内容简介】

《确定性系统的统计性质》介绍的是确定性离散动力系统统计性质的基本理论与计算方法，首先介绍了遍历理论的一些经典结果；然后着重研究了对应于混沌映射的绝对连续不变测度的存在性与计算问题，这归结于相应的Frobenius—Perron算子的泛函分析与数值分析；最后《确定性系统的统计性质》介绍了Shannon熵、Kolmogorov熵、拓扑熵以及Boltzmann熵，并给出了不变测度的一些最新应用。《确定性系统的统计性质》可作为数学、计算科学及工程专业的研究生教材或参考书。

【目录】

Chapter1Introduction
1.1DiscreteDeterministicSystems—fromOrdertoChaos
1.2StatisticalStudyofChaos
Exercises

Chapter2FoundationsofMeasureTheory
2.1MeasuresandIntegration
2.2BasicIntegrationTheory
2.3FunctionsofBoundedVariationinOneVariable
2.4FunctionsofBoundedVariationinSeveralVariables
2.5CompactnessandQuasi—compactness
2.5.1StrongandWleakCompactness
2.5.2Quasi-Compactness
Exercises

Chapter3RudimentsofErgodicTheory
3.1MeasurePreservingTransfcIrmations
3.2Ergodicity,MixingandExactness
3.2.1Ergodicity
3.2.2MixingandExactness
3.3ErgodicTheorems
3.4TopologicalDynamicalSystems
Exercises

Chapter4Frobenius-PerronOperators
4.1MarkovOperatorst
4.2nobenius—PerronOperators
4.3Koopman0peratorst
4.4ErgodicityandFrobenius—PerronOperators
4.5DecompositionTheoremandSpectralAnalysis
Exercises

Chapter5InvariantMeasures——Existence
5.1GeneralExistenceResults
5.2PiecewiseStretchingMappings
5.3PiecewiseConvexMappings
5.4PiecewiseExpandingTransformations
Exercises

Chapter6InvariantMeasures--Computation
61Ulam’sMethodforOne—DimensionalMappings
6.2Ulam’SMethodforN—dimensionalTransformations
6.3TheMarkovMethodforOne—DimensionalMappings
6.4TheMarkovMetho（~forN—dimensionalTransformations
Exercises

Chapter7ConvergenceRateAnalysis
7.1ErrorEstimatesforUlam’SMethod.
7.2MoreExplicitErrorEstimates
7.3ErrorEstimatesfortheMarkovMethod
Exercises

Chapter8Entropy
8.1ShannonEntropy
8.2KolmogorovEntropy
8.3TopologicalEntropy
8.4BoltzmannEntropy
8.5BoltzmannEntropyandFrobenius—PerronOperators
Exercises

Chapter9ApplicationsofInvariantMeasures
9.1DecayofCorrelations
9.2RandomNumberGenerationi
9.3ConformationalDynamicsofBio—molecules4：
9.4DS—CDMAinWirelessCommunications
Exercises
Bibliography
Index