文档介绍：CONTENTS
Chapter I. Introduction and examples 1
Examples 1
Isomorphism 5
Exercises 8
Chapter II. Fourier analysis on groups 12
Introduction 12
Dual groups, Fourier transforms 13
Pontryagin duality 15
Examples 16
Exercises 16
Chapter III. Measure theoretic entropy 19
Partitions and algebras 19
Entropy of partitions 20
Conditional entropy 21
Entropy of a measure–preserving transformation 22
Exercises 23
Chapter IV. Properties of metric entropy 25
Powers of transformations 25
Zero entropy 25
Calculating h(T ): theory 26
Calculating h(T ): examples 28
Exercises 29
Chapter V. Entropy as an invariant 30
Non–isomorphic maps with the same entropy 30
Kolmogorov and Bernoulli automorphisms 31
The Pinsker algebra 34
Exercises 35
Chapter VI. Topological entropy I: definitions 37
Bowen’s definition 37
Definition using open covers 39
When the two definitions coincide 40
Exercises 42
Chapter VII. Topological entropy II: homogeneous mea-
sures 43
A topological Kolmogorov–Sinai type theorem 43
Examples 45
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Homogeneous measures 46
The variational principle 50
Linear maps and covering spaces 50
Exercises 52
Chapter VIII. Topological entropy III: Yuzvinskii’s for-
mula 55
The adele ring 55
Automorphisms of solenoids 56
Generalizing Theorem