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正版新书]遍历性理论引论(英文版)Peter Walters|责编:刘慧//高
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Chapter 0 Preliminaries
§0.1 Introduction
§0.2 Measure Spaces
§0.3 Integration
§0.4 Absolutely Continuous Measures and Conditional Expectations
§0.5 Function Spaces
§0.6 Haar Measure
§0.7 Character Theory
§0.8 Endomorphisms of Tori
§0.9 Perron-Frobenius Theory
Chapter 1 Measure-Preserving Transformations
§1.1 Definition and Examples
§1.2 Problems in Ergodic Theory
§1.3 Associated Isometries
§1.4 Recurrence
§1.5 Ergodicity
§1.6 The Ergodic Theorem
§1.7 Mixing
Chapter 2 Isomorphism, Conjugacy, and Spectral Isomorphism
§2.1 Point Maps and Set Maps
§2.2 Isomorphism of Measure-Preserving Transformations
§2.3 Conjugacy of Measure-Preserving Transformations
§2.4 The Isomorphism Problem
§2.5 Spectral Isomorphism
§2.6 Spectral Invariants
Chapter 3 Measure-Preserving Transformations with Discrete Spectrum
§3.1 Eigenvalues and Eigenfunctions
§3.2 Discrete Spectrum
§3.3 Group Rotations
Chapter 4 Entropy
§4.1 Partitions and Subalgebras
§4.2 Entropy of a Partition
§4.3 Conditional Entropy
§4.4 Entropy of a Measure-Preserving Transformation
§4.5 Properties of h (T, A)and h (T)
§4.6 Some Methods for Calculating h (T)
§4.7 Examples
§4.8 How Good an Invariant is Entropy?
§4.9 Bernoulli Automorphisms and Kolmogorov Automorphisms
§4.10 The Pinsker o-Algebra of a Measure-Preserving Transformation
§4.11 Sequence Entropy
§4.12 Non-invertible Transformations
§4.13 Comments
Chapter 5 Topological Dynamics
§5.1 Examples
§5.2 Minimality
§5.3 The Non-wandering Set
§5.4 Topological Transitivity
§5.5 Topological Conjugacy and Discrete Spectrum
§5.6 Expansive Homeomorphisms
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