确定性系统的统计性质
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作者丁玖,周爱辉 编著
出版社清华大学出版社
ISBN9787302182962
出版时间2008-11
版次1
装帧精装
开本16开
纸张胶版纸
页数236页
字数99999千字
定价48元
上书时间2024-05-07
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基本信息
书名:确定性系统的统计性质
定价：48元
作者:丁玖,周爱辉 编著
出版社：清华大学出版社
出版日期：2008-11-01
ISBN：9787302182962
字数：355000
页码：236
版次：1
装帧：精装
开本：16开
商品重量：
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内容提要
本书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；最后本书介绍了Shannon熵、Kolmogorov熵、拓扑熵以及Boltzmann熵，并给出了不变测度的一些应用．本书可作为数学、计算科学及工程专业的研究生教材或参考书。
目录
Chapter 1 Introduction 1.1 Discrete Deterministic Systems—from Order to Chaos 1.2 Statistical Study of Chaos ExercisesChapter 2 Foundations of Measure Theory 2.1 Measures and Integration 2.2 Basic Integration Theory 2.3 Functions of Bounded Variation in One Variable 2.4 Functions of Bounded Variation in Several Variables 2.5 Compactness and Quasi—compactness 2.5.1 Strong and Wleak Compactness 2.5.2 Quasi-Compactness ExercisesChapter 3 Rudiments of Ergodic Theory 3.1 Measure Preserving TransfcIrmations 3.2 Ergodicity,Ming and Exactness 3.2.1 Ergodicity 3.2.2 Ming and Exactness 3.3 Ergodic Theorems 3.4 Topological Dynamical Systems ExercisesChapter 4 Frobenius-Perron Operators 4.1 Markov Operatorst 4.2 nobenius—Perron Operators 4.3 Koopman 0peratorst 4.4 Ergodicity and Frobenius—Perron Operators 4.5 Decomposition Theorem and Spectral Analysis ExercisesChapter 5 Invariant Measures——Estence 5.1 General Estence Results 5.2 Piecewise Stretching Mappings 5.3 Piecewise Convex Mappings 5.4 Piecewise Expanding Transformations Exercises.Chapter 6 Invariant Measures--Computation 61 Ulam’s Method for One—Dimensional Mappings 6.2 Ulam’S Method for N—dimensional Transformations 6.3 The Markov Method for One—Dimensional Mappings 6.4 The Markov Metho(~for N—dimensional Transformations Exercises-Chapter 7 Convergence Rate Analysis 7.1 Error Estimates for Ulam’S Method. 7.2 More Explicit Error Estimates 7.3 Error Estimates for the Markov Method ExercisesChapter 8 Entropy 8.1 Shannon Entropy 8.2 Kolmogorov Entropy 8.3 Topological Entropy 8.4 Boltzmann Entropy 8.5 Boltzmann Entropy and Frobenius—Perron Operators ExercisesChapter 9 Applications of Invariant Measures 9.1 Decay of Correlations 9.2 Random Number Generationi 9.3 Conformational Dynamics of Bio—molecules4： 9.4 DS—CDMA in Wireless Communications ExercisesBibliographyIndex
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