國外數學名著係列73（影印版）：混沌動力係統的概念和結果 [Concepts and Results in Chaotic Dynamics：A Short Course] pdf epub mobi txt 電子書 下載 2025

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Pierre，Collet，Jean-Pierre，Eckmann 著

齣版社： 科學齣版社有限責任公司

ISBN：9787030313898

版次：1

商品編碼：11895613

包裝：精裝

叢書名： 國外數學名著係列（影印版）73

外文名稱：Concepts and Results in Chaotic Dynamics：A Short Course

開本：16開

齣版時間：2011-06-01

用紙：膠版紙#

內容簡介

　　《國外數學名著係列73（影印版）：混沌動力係統的概念和結果》是“國外數學名著係列”之一，介紹瞭混沌動力係統的概念和其拓撲性質、雙麯率、不變測度、熵和其他概率結果。
　　《國外數學名著係列73（影印版）：混沌動力係統的概念和結果》適閤高等院校數學係研究生、數學科研人員學習參考。

內頁插圖

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

前言/序言

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