包邮遍历性理论引论

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
　0.10 Topology
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 Transformhtions
　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 orb 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 -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
Chapter 6 Invariant Measures for Continuous Transformations
　6.1 Measures on Metric Spaces
　6.2 Invariant Measures for Continuous Transformations
　6.3 Interpretation of Ergodicity and Mixing
　6.4 Relation of Invariant Measures to Non-wandering Sets, Periodic Points and Topological Transitivity
6.5 Unique Ergodicity
6.6 Examples
Chapter 7 Topological Entropy
　7.1 Definition Using Open Covers
　7.2 Bowen's Definition
　7.3 Calculation of Topological Entropy
Chapter 8 Relationship Between Topological Entropy and Measure-Theoretic Entropy
　8.1 The Entropy Map
　8.2 The Variational Principle
　8.3 Measures with Maximal Entropy
　8.4 Entropy of Affine Transformations
　8.5 The Distribution of Periodic Points
　8.6 Definition of Measure-Theoretic Entropy Using the Metrics dn
Chapter 9 Topological Pressure and Its Relationship with Invariant Measures
　9.1 Topological Pressure
　9.2 Properties of Pressure
　9.3 The Variational Principle
　9.4 Pressure Determines M X, T
　9.5 Equilibrium States
Chapter 10 Applications and Other Topics
　10.1 The Qualitative Behaviour of Diffeomorphisms
　10.2 The Subadditive Ergodic Theorem and the Multiplicative Ergodic Theorem
　10.3 Quasi-invariant Measures
　10.4 Other Types of Isomorphism
　10.5 Transformations of Intervals
　10.6 Further Reading
References
Index