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無窮遍歷理論引論(英文版)(精)/美國數學會經典影印系列

  • 作者：(以)喬恩·阿倫森|責編:李鵬
  • 出版社：高等教育
  • ISBN：9787040630954
  • 出版日期：2025/02/01
  • 裝幀：精裝
  • 頁數：284
人民幣：RMB 135 元      售價：元
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內容大鋼
    無窮遍歷理論是研究無窮測度空間中的保測變換的理論。本書著重介紹了無窮保測變換的特殊性質。本書適合對遍歷理論、動力系統和概率論感興趣的研究生以及數學研究人員閱讀參考。
作者介紹
(以)喬恩·阿倫森|責編:李鵬
目錄
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  Induced transformations
  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  Converse to Birkhoff's theorem
  2.4  Transformations with infinite invariant measures
  2.5  Structure of measure - preserving transformations
  2.6  Eigenvalues and eigenfunctions
  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  Infinite ergodic theorems
  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 Frobenius–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 geodesics
  7.4  Surfaces
  7.5  The Poincar? 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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