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无穷遍历理论引论（影印版）

样章
作者：
Jon Aaronson
定价：
135.00元
ISBN：
978-7-04-063095-4
版面字数：
475.00千字
开本：
特殊
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2025-02-14
物料号：
63095-00
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
  • 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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