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确定性系统的统计性质
作者：丁玖，周爱辉 编著
出版社：清华大学出版社
出版时间：2008-11-01
ISBN：9787302182962
定价：¥48.00
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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。
作者简介
Jiu Ding，Aihui Zhou，Statistical Properties of Deterministic SystemsStatistical Properties of Deterministic Systems discusses the fundamental theory and computational methods of the statistical properties of deterministic discrete dynamical systems. After introducing some basic results from ergodic theory， two probIems related to the dynamical system are studied： first the existence of absolute continuous invariant measures， and then their computation. They correspond to the functional analysis and numerical analysis of the Frobenius-Perron operator associated with the dynamical system.The book can be used as a text for graduate students in applied mathematics and in computational mathematics; it can also serve as a reference book for researchers in the physical sciences， life sciences， and engineering.
目录
Chapter 1 Introduction
1.1 Discrete Deterministic Systems—from Order to Chaos
1.2 Statistical Study of Chaos
Exercises
Chapter 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
Exercises
Chapter 3 Rudiments of Ergodic Theory
3.1 Measure Preserving TransfcIrmations
3.2 Ergodicity,Mixing and Exactness
3.2.1 Ergodicity
3.2.2 Mixing and Exactness
3.3 Ergodic Theorems
3.4 Topological Dynamical Systems
Exercises
Chapter 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
Exercises
Chapter 5 Invariant Measures——Existence
5.1 General Existence 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
Exercises
Chapter 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
Exercises
Chapter 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
Exercises
Bibliography
Index
1.1 Discrete Deterministic Systems—from Order to Chaos
1.2 Statistical Study of Chaos
Exercises
Chapter 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
Exercises
Chapter 3 Rudiments of Ergodic Theory
3.1 Measure Preserving TransfcIrmations
3.2 Ergodicity,Mixing and Exactness
3.2.1 Ergodicity
3.2.2 Mixing and Exactness
3.3 Ergodic Theorems
3.4 Topological Dynamical Systems
Exercises
Chapter 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
Exercises
Chapter 5 Invariant Measures——Existence
5.1 General Existence 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
Exercises
Chapter 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
Exercises
Chapter 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
Exercises
Bibliography
Index
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