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遍历性理论引论PDF|Epub|txt|kindle电子书版本网盘下载
- PETER WALTERS 著
- 出版社： SPRINGER-VERLAG
- ISBN：7506201097
- 出版时间：2000
- 标注页数：252页
- 文件大小：98MB
- 文件页数：40279871页
- 主题词：
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图书目录
Chapter 0 Preliminaries1
0.1 Introduction1
0.2 Measure Spaces3
0.3 Integrationry6
0.4 Absolutely Continuous Measures and Conditional Expectations8
0.5 Function Spaces9
0.6 Haar Measure11
0.7 Character Theory12
0.8 Endomorphisms of Tori14
0.9 Perron-Frobenius Theory16
0.10 Topology17
Chapter 1 Measure-Preserving Transformations19
1.l Definition and Examples19
1.2 Problems in Ergodic Theory23
1.3 Associated Isometrics24
1.4 Recurrence26
1.5 Ergodicity26
1.6 The Ergodic Theorem34
1.7 Mixing39
Chapter 2 Isomorphism, Conjugacy, and Spectral Isomorphism53
2.1 Point Maps and Set Maps53
2.2 Isomorphism of Measure-Preserving Transformations57
2.3 Conjugacy of Measure-Preserving Transformations59
2.4 The Isomorphism Problem62
2.5 Spectral Isomorphism63
2.6 Spectral Invariants66
Chapter 3 Measure-Preserving Transformations with Discrete Spectrum68
3.1 Eigenvalues and Eigenfunctions68
3.2 Discrete Spectrum69
3.3 Group Rotations72
Chapter 4 Entropy75
4.1 Partitions and Subalgebras75
4.2 Entropy of a Partition77
4.3 Conditional Entropy80
4.4 Entropy of a Measure-Preserving Transformation86
4.5 Properties of h（T,？） and h（T）89
4.6 Some Methods for Calculating h（T）94
4.7 Examples100
4.8 How Good an Invariant is Entropy?103
4.9 Bernoulli Automorphisms and Kolmogorov Automorphisms105
4.10 The Pinsker σ-Algebra of a Measure-Preserving Transformation113
4.11 Sequence Entropy114
4.12 Non-invertible Transformations115
4.13 Comments116
Chapter 5 Topological Dynamics118
5.1 Examples118
5.2 Minimality120
5.3 The Non-wandering Set123
5.4 Topological Transitivity127
5.5 Topological Conjugacy and Discrete Spectrum133
5.6 Expansive Homeomorphisms137
Chapter 6 Invariant Measures for Continuous Transformations146
6.1 Measures on Metric Spaces146
6.2 Invariant Measures for Continuous Transformations150
6.3 Interpretation of Ergodicity and Mixing154
6.4 Relation of Invariant Measures to Non-wandering Sets, Periodic Points and Topological Transitivity156
6.5 Unique Ergodicity158
6.6 Examples162
Chapter 7 Topological Entropy164
7.1 Definition Using Open Covers164
7.2 Bowen's Definition168
7.3 Calculation of Topological Entropy176
Chapter 8 Relationship Between Topological Entropy and Measure-Theoretic Entropy182
8.1 The Entropy Map182
8.2 The Variational Principle187
8.3 Measures with Maximal Entropy191
8.4 Entropy of Affine Transformations196
8.5 The Distribution of Periodic Points203
8.6 Definition of Measure-Theoretic Entropy Using the Metrics dn205
Chapter 9 Topological Pressure and Its Relationship with Invariant Measures207
9.1 Topological Pressure207
9.2 Properties of Pressure214
9.3 The Variational Principle217
9.4 Pressure Determines M（X,T）221
9.5 Equilibrium States223
Chapter 10 Applications and Other Topics229
10.1 The Qualitative Behaviour of Difleomorphisms229
10.2 The Subadditive Ergodic Theorem and the Multiplicative Ergodic Theorem230
10.3 Quasi-invariant Measures236
10.4 Other Types of Isomorphism238
10.5 Transformations of Intervals238
10.6 Further Reading239
References240
Index247