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作 者：（法国）克莱（Collrt），（瑞士）艾克曼（Eckmann，J-P） 著
出 版 社：科学出版社
出版时间：2011-06-01
I S B N：9787030313898
| The study of dynamical systems is a well established field. Having given graduate-level courses on the subject for many years，the authors have now written this book to provide a panorama of the aspects that are of interest to mathematicians and physicists alike。Avoiding belaboured proofs，the exposition concentrates instead on abundant illustrations and examples，while still retaining sufficient mathematical precision. Besides the standard topics of the field，questions of physical measurement and stochastic properties of chaotic dynamical system are given much attention. |
| 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 |
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