《混沌動力系統的概念和結果》是2011年6月1日科學出版社出版的一本圖書，作者是PierreCollet。
基本介紹
- 書名：混沌動力系統的概念和結果
- 作者：PierreCollet
- ISBN：9787030313898
- 定價： 68.00元
- 出版社：科學出版社
- 出版時間：2011年6月1日
- 開本：16開
內容簡介,圖書目錄,
內容簡介
本書介紹了混沌動力系統的概念和其拓撲性質、雙曲率、不變測度、熵和其他機率結果。
圖書目錄
1 A Basic Problem
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
