无穷遍历理论引论（影印版）

样章

作者：

Jon Aaronson

定价：

135.00 元

版面字数：

475千字

开本：

特殊

装帧形式：

精装

版次：

最新版次
印刷时间：

2025年

ISBN：

978-7-04-063095-4

物料号：

63095-00

出版时间：

2025-02-14

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

动力系统

暂无

目录
- 前辅文
- Preface
- Chapter 1. Non-singular transformations
  - §1.0 Standard measure spaces
  - §1.1 Recurrence and conservativity
  - §1.2 Ergodicity
  - §1.3 The dual operator
  - §1.4 Invariant measures
  - §1.5 Induced transformations and applications
  - §1.6 Group actions and flows
- Chapter 2. General ergodic and spectral theorems
  - §2.1 von Neumann's mean ergodic theorem
  - §2.2 Pointwise ergodic theorems
  - §2.3 Converses to Birkhoff's theorem
  - §2.4 Transformations with infinite invariant measures
  - §2.5 Spectral properties
  - §2.6 Eigenvalues
  - §2.7 Ergodicity of Cartesian products
- Chapter 3. Transformations with infinite invariant measures
  - §3.1 Isomorphism, factors, and similarity
  - §3.2 Intrinsic normalising constants and laws of large numbers
  - §3.3 Rational ergodicity
  - §3.4 Maharam transformations
  - §3.5 Category theorems
  - §3.6 Asymptotic distributional behaviour
  - §3.7 Pointwise dual ergodicity
  - §3.8 Wandering rates
- Chapter 4. Markov maps
  - §4.1 Markov partitions
  - §4.2 Graph shifts
  - §4.3 Distortion properties
  - §4.4 Ergodic properties of Markov maps with distortion properties
  - §4.5 Markov shifts
  - §4.6 Schweiger's jump transformation
  - §4.7 Smooth Probenius-Perron operators and the Gibbs property
  - §4.8 Non-expanding interval maps
  - §4.9 Additional reading
- Chapter 5. Recurrent events and similarity of Markov shifts
  - §5.1 Renewal sequences
  - §5.2 Markov towers and recurrent events
  - §5.3 Kaluza sequences
  - §5.4 Similarity of Markov towers
  - §5.5 Random walks
- Chapter 6. Inner functions
  - §6.1 Inner functions on the unit disc
  - §6.2 Inner functions on the upper half plane
  - §6.3 The dichotomy
  - §6.4 Examples
- Chapter 7. Hyperbolic geodesic flows
  - §7.1 Hyperbolic space models
  - §7.2 The geodesic flow of H
  - §7.3 Asymptotic geodesies
  - §7.4 Surfaces
  - §7.5 The Poincare series
  - §7.6 Further results
- Chapter 8. Cocycles and skew products
  - §8.1 Skew Products
  - §8.2 Persistencies and essential values
  - §8.3 Coboundaries
  - §8.4 Skew products over Kronecker transformations
  - §8.5 Joinings of skew products
  - §8.6 Squashable skew products over odometers
- Bibliography
- Index

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