Chapter 1 Introduction
1.1 Discrete Deterministic Systems—from Order to Chaos
1.2 Statistical Study of Chaos
Exercises
Chapter 2 Foundations of Measure Theory
2.1 Measures and Integration
2.2 Basic Integration Theory
2.3 Functions of Bounded Variation in One Variable
2.4 Functions of Bounded Variation in Several Variables
2.5 Compactness and Quasi—compactness
2.5.1 Strong and Wleak Compactness
2.5.2 Quasi-Compactness
Exercises
Chapter 3 Rudiments of Ergodic Theory
3.1 Measure Preserving TransfcIrmations
3.2 Ergodicity,Mixing and Exactness
3.2.1 Ergodicity
3.2.2 Mixing and Exactness
3.3 Ergodic Theorems
3.4 Topological Dynamical Systems
Exercises
Chapter 4 Frobenius-Perron Operators
4.1 Markov Operatorst
4.2 nobenius—Perron Operators
4.3 Koopman 0peratorst
4.4 Ergodicity and Frobenius—Perron Operators
4.5 Decomposition Theorem and Spectral Analysis
Exercises
Chapter 5 Invariant Measures——Existence
5.1 General Existence Results
5.2 Piecewise Stretching Mappings
5.3 Piecewise Convex Mappings
5.4 Piecewise Expanding Transformations
Exercises.
Chapter 6 Invariant Measures--Computation
61 Ulam’s Method for One—Dimensional Mappings
6.2 Ulam’S Method for N—dimensional Transformations
6.3 The Markov Method for One—Dimensional Mappings
6.4 The Markov Metho(~for N—dimensional Transformations
Exercises-
Chapter 7 Convergence Rate Analysis
7.1 Error Estimates for Ulam’S Method.
7.2 More Explicit Error Estimates
7.3 Error Estimates for the Markov Method
Exercises
Chapter 8 Entropy
8.1 Shannon Entropy
8.2 Kolmogorov Entropy
8.3 Topological Entropy
8.4 Boltzmann Entropy
8.5 Boltzmann Entropy and Frobenius—Perron Operators
Exercises
Chapter 9 Applications of Invariant Measures
9.1 Decay of Correlations
9.2 Random Number Generationi
9.3 Conformational Dynamics of Bio—molecules4：
9.4 DS—CDMA in Wireless Communications
Exercises
Bibliography
Index
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