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Pierre,Collet,Jean-Pierre,Eckmann 著
出版社: 科学出版社有限责任公司 ISBN:9787030313898 版次:1 商品编码:11895613 包装:精装 丛书名: 国外数学名著系列(影印版)73 外文名称:Concepts and Results in Chaotic Dynamics:A Short Course 开本:16开 出版时间:2011-06-01 用纸:胶版纸#
《国外数学名著系列73(影印版):混沌动力系统的概念和结果》适合高等院校数学系研究生、数学科研人员学习参考。
2 Dynamical Systems
2.1 Basics of Mechanical Systems
2.2 Formal Definitions
2.3 Maps
2.4 Basic Examples of Maps
2.5 More Advanced Examples
2.6 Examples of Flows
3 Topological Properties
3.1 Coding, Kneading
3.2 Topological Entropy
3.2.1 Topological, Measure, and Metric Spaces
3.2.2 Some Examples
3.2.3 General Theory of Topological Entropy
3.2.4 A Metric Version of Topological Entropy
3.3 Attractors
4 Hyperbolicity
4.1 Hyperbolic Fixed Points
4.1.1 Stable and Unstable Manifolds
4.1.2 Conjugation
4.1.3 Resonances
4.2 Invariant Manifolds
4.3 Nonwandering Points and Axiom A Systems
4.4 Shadowing and Its Consequences
4.4.1 Sensitive Dependence on Initial Conditions
4.4.2 Complicated Orbits Occur in Hyperbolic Systems
4.4.3 Change of Map
4.5 Construction of Markov Partitions
5 Invariant Measures
5.1 Overview
5.2 Details
5.3 The Perron-Frobenius Operator
5.4 The Ergodic Theorem
5.5 Convergence Rates in the Ergodic Theorem
5.6 Mixing and Decay of Correlations
5.7 Physical Measures
5.8 Lyapunov Exponents
6 Entropy
6.1 The Shannon-McMillan-Breiman Theorem
6.2 Sinai-Bowen-Ruelle Measures
6.3 Dimensions
7 Statistics and Statistical Mechanics
7.1 The Central Limit Theorem
7.2 Large Deviations
7.3 Exponential Estimates
7.3. I Concentration
7.4 The Formalism of Statistical Mechanics
7.5 Multifractal Measures
8 Other Probabilistic Results
8.1 Entrance and Recurrence Times
8.2 Number of Visits to a Set
8.3 Extremes
8.4 Quasi-lnvariant Measures
8.5 Stochastic Perturbations
9 Experimental Aspects
9.1 Correlation Functions and Power Spectrum
9.2 Resonances
9.3 Lyapunov Exponents
9.4 Reconstruction
9.5 Measuring the Lyapunov Exponents
9.6 Measuring Dimensions
9.7 Measuring Entropy
9.8 Estimating the Invariant Measure
References
Index
国外数学名著系列73(影印版):混沌动力系统的概念和结果 [Concepts and Results in Chaotic Dynamics:A Short Course] 电子书 下载 mobi epub pdf txt
国外数学名著系列73(影印版):混沌动力系统的概念和结果 [Concepts and Results in Chaotic Dynamics:A Short Course]-so88
国外数学名著系列73(影印版):混沌动力系统的概念和结果 [Concepts and Results in Chaotic Dynamics:A Short Course] pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
Pierre,Collet,Jean-Pierre,Eckmann 著
出版社: 科学出版社有限责任公司 ISBN:9787030313898 版次:1 商品编码:11895613 包装:精装 丛书名: 国外数学名著系列(影印版)73 外文名称:Concepts and Results in Chaotic Dynamics:A Short Course 开本:16开 出版时间:2011-06-01 用纸:胶版纸#
内容简介
《国外数学名著系列73(影印版):混沌动力系统的概念和结果》是“国外数学名著系列”之一,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。《国外数学名著系列73(影印版):混沌动力系统的概念和结果》适合高等院校数学系研究生、数学科研人员学习参考。
内页插图
目录
1 A Basic Problem2 Dynamical Systems
2.1 Basics of Mechanical Systems
2.2 Formal Definitions
2.3 Maps
2.4 Basic Examples of Maps
2.5 More Advanced Examples
2.6 Examples of Flows
3 Topological Properties
3.1 Coding, Kneading
3.2 Topological Entropy
3.2.1 Topological, Measure, and Metric Spaces
3.2.2 Some Examples
3.2.3 General Theory of Topological Entropy
3.2.4 A Metric Version of Topological Entropy
3.3 Attractors
4 Hyperbolicity
4.1 Hyperbolic Fixed Points
4.1.1 Stable and Unstable Manifolds
4.1.2 Conjugation
4.1.3 Resonances
4.2 Invariant Manifolds
4.3 Nonwandering Points and Axiom A Systems
4.4 Shadowing and Its Consequences
4.4.1 Sensitive Dependence on Initial Conditions
4.4.2 Complicated Orbits Occur in Hyperbolic Systems
4.4.3 Change of Map
4.5 Construction of Markov Partitions
5 Invariant Measures
5.1 Overview
5.2 Details
5.3 The Perron-Frobenius Operator
5.4 The Ergodic Theorem
5.5 Convergence Rates in the Ergodic Theorem
5.6 Mixing and Decay of Correlations
5.7 Physical Measures
5.8 Lyapunov Exponents
6 Entropy
6.1 The Shannon-McMillan-Breiman Theorem
6.2 Sinai-Bowen-Ruelle Measures
6.3 Dimensions
7 Statistics and Statistical Mechanics
7.1 The Central Limit Theorem
7.2 Large Deviations
7.3 Exponential Estimates
7.3. I Concentration
7.4 The Formalism of Statistical Mechanics
7.5 Multifractal Measures
8 Other Probabilistic Results
8.1 Entrance and Recurrence Times
8.2 Number of Visits to a Set
8.3 Extremes
8.4 Quasi-lnvariant Measures
8.5 Stochastic Perturbations
9 Experimental Aspects
9.1 Correlation Functions and Power Spectrum
9.2 Resonances
9.3 Lyapunov Exponents
9.4 Reconstruction
9.5 Measuring the Lyapunov Exponents
9.6 Measuring Dimensions
9.7 Measuring Entropy
9.8 Estimating the Invariant Measure
References
Index
前言/序言
国外数学名著系列73(影印版):混沌动力系统的概念和结果 [Concepts and Results in Chaotic Dynamics:A Short Course] 电子书 下载 mobi epub pdf txt
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