混沌动力系统的概念和结果 内容简介

本书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。

混沌动力系统的概念和结果 本书特色

科莱和埃克曼合著的《混沌动力系统的概念和结果（影印版）》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。适合高等院校数学系研究生、数学科研人员学习参考。

混沌动力系统的概念和结果 目录

1A Basic Problem2Dynamical Systems2.1Basics of Mechanical Systems2.2Formal Definitions2.3Maps2.4Basic Examples of Maps2.5More Advanced Examples2.6Examples of Flows3Topological Properties3.1Coding, Kneading3.2Topological Entropy3.2.1Topological, Measure, and Metric Spaces3.2.2Some Examples3.2.3General Theory of Topological Entropy3.2.4A Metric Version of Topological Entropy3.3Attractors4Hyperbolicity4.1Hyperbolic Fixed Points4.1.1Stable and Unstable Manifolds4.1.2Conjugation4.1.3Resonances4.2Invariant Manifolds4.3Nonwandering Points and Axiom A Systems4.4Shadowing and Its Consequences4.4.1Sensitive Dependence on Initial Conditions4.4.2Complicated Orbits Occur in Hyperbolic Systems4.4.3Change of Map4.5Construction of Markov Partitions5Invariant Measures5.1Overview5.2Details5.3The Perron-Frobenius Operator5.4The Ergodic Theorem5.5Convergence Rates in the Ergodic Theorem5.6Mixing and Decay of Correlations5.7Physical Measures5.8Lyapunov Exponents6Entropy6.1The Shannon-McMillan-Breiman Theorem6.2Sinai-Bowen-Ruelle Measures6.3Dimensions7Statistics and Statistical Mechanics7.1The Central Limit Theorem7.2Large Deviations7.3Exponential Estimates7.3. IConcentration7.4The Formalism of Statistical Mechanics7.5Multifractal Measures8Other Probabilistic Results8.1Entrance and Recurrence Times8.2Number of Visits to a Set8.3Extremes8.4Quasi-lnvariant Measures8.5Stochastic Perturbations9Experimental Aspects9.1Correlation Functions and Power Spectrum9.2Resonances9.3Lyapunov Exponents9.4Reconstruction9.5Measuring the Lyapunov Exponents9.6Measuring Dimensions9.7Measuring Entropy9.8Estimating the Invariant MeasureReferencesIndex