1 A Basic Problem 2 Dynamical Systems 2.1 Basics of Mechanical Systems 2.2 Formal Defingions 2.3 Maps 2.4 Basic Examples of Maps 2.5 More Advanced Examples 2.6 Examples of Flows 3 Topologieal 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 Hyperbolieity 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 Nonwandefing 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 Etgodic Theorem 5.6 Mixing and Decay of Correlations 5.7 Physical Measures 5.8 Lyapunov Exponents 6 Entropy 6.1 The Shannon-McMillan-B reiman 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 7.3.1 Concentration 7.4 The Formalism of Staistical Mechanics 7.5 Mulfifractal 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-Invariant 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 Measuringthe Lyapunov Exponents 9.6 Measuring Dimensions 9.7 Measuring Entropy 9.8 Estimating the Invafiant Measure References Index
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