全書分兩部分內(nèi)容：（一）討論概率空間變換理論的測度論內(nèi)容，包括遞歸性質(zhì)、混合性質(zhì)、Birkhoff遍歷性定理、同構(gòu)性和譜性質(zhì)、熵理論等；（二）討論緊致可測空間中的連續(xù)變換的遍歷性理論。
目次：測度保形變換; 同構(gòu)、共軛、譜同構(gòu)；具有離散譜的測度變換；熵；拓?fù)鋭討B(tài)學(xué)；連續(xù)變換的不變測度；拓?fù)潇丶捌渑c測度理論熵的關(guān)系；拓?fù)鋲嚎s及其不變測度的關(guān)系；有關(guān)應(yīng)用及其他課題。
讀者對象：概率論及相關(guān)專業(yè)的研究生及數(shù)學(xué)工作者。
Chapter 0 Preliminaries
0.1 Introdu*ion
0.2 Measure Spaces
0.3 Integr*ion
0.4 Absolutely Continuous Measures and Conditional Expe**ions
0.5 Fun*ion Spaces
0.6 Haar Measure
0.7 Chara*er Theory
0.8 Endomorphisms of Tori
0.9 Perron-Frobenius Theory
0.10 Topology
Chapter 1 Measure-Preserving Transfor*tions
1.1 Definition and Examples
1.2 Problems in Ergodic Theory
1.3 Associ*ed Isometries
1.4 Recurrence
1.5 Ergodicity
1.6 The Ergodic Theorem
1.7 Ming
Chapter 2 Isomorphism, Con*ugacy, and Spe*ral Isomorphism
2.1 Point Maps and Set Maps
2.2 Isomorphism of Measure-Preserving Transfor*tions
2.3 Con*ugacy of Measure-preserving Transformhtions
2.4 The Isomorphism Problem
2.5 Spe*ral Isomorphism
2.6 Spe*ral Invariants
Chapter 3 Measure-Preserving Transfor*tions with Discrete Spe*rum
3.1 Eigenvalues and Eigenfun*ions
3.2 Discrete Spe*rum
3.3 Group Rot*ions
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 Transfor*tion
4.5 Properties orb T,A and h T
4.6 Some Methods for Calcul*ing 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 Transfor*tion
4.11 Sequence Entropy
4.12 Non-invertible Transfor*tions
4.13 Comments
Chapter 5 Topological Dynamics
5.1 Examples
5.2 Mini*lity
5.3 The Non-wandering Set
5.4 Topological Transitivity
5.5 Topological Con*ugacy and Discrete Spe*rum
5.6 Expansive Homeomorphisms
Chapter 6 Invariant Measures for Continuous Transfor*tions
6.1 Measures on Metric Spaces
6.2 Invariant Measures for Continuous Transfor*tions
6.3 Interpret*ion of Ergodicity and Ming
6.4 Rel*ion 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 Cove*
7.2 Bowen's Definition
7.3 Calcul*ion of Topological Entropy
Chapter 8 Rel*ionship Between Topological Entropy and Measure-Theoretic Entropy
8.1 The Entropy Map
8.2 The Vari*ional Principle
8.3 Measures with Ma*l Entropy
8.4 Entropy of Affine Transfor*tions
8.5 The Distribution of Periodic Points
8.6 Definition of Measure-Theoretic Entropy Using the Metrics dn
Chapter 9 Topological Pressure and Its Rel*ionship with Invariant Measures
9.1 Topological Pressure
9.2 Properties of Pressure
9.3 The Vari*ional Principle
9.4 Pressure Determines M X, T
9.5 Equilibrium St*es
Chapter 10 Applic*ions and Other Topics
10.1 The Qualit*ive Behaviour of Diffeomorphisms
10.2 The Subadditive Ergodic Theorem and the Multiplic*ive Ergodic Theorem
10.3 Quasi-invariant Measures
10.4 Other Types of Isomorphism
10.5 Transfor*tions of Intervals
10.6 Further Reading
References
Index
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