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Weakly Wandering Sequences in Ergodic Theory

  • Stanley Eigen
  • Arshag Hajian
  • Yuji Ito
  • Vidhu Prasad

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Stanley Eigen, Arshag Hajian, Yuji Ito, Vidhu Prasad
    Pages 1-16
  3. Stanley Eigen, Arshag Hajian, Yuji Ito, Vidhu Prasad
    Pages 17-24
  4. Stanley Eigen, Arshag Hajian, Yuji Ito, Vidhu Prasad
    Pages 25-39
  5. Stanley Eigen, Arshag Hajian, Yuji Ito, Vidhu Prasad
    Pages 41-63
  6. Stanley Eigen, Arshag Hajian, Yuji Ito, Vidhu Prasad
    Pages 65-77
  7. Stanley Eigen, Arshag Hajian, Yuji Ito, Vidhu Prasad
    Pages 79-102
  8. Stanley Eigen, Arshag Hajian, Yuji Ito, Vidhu Prasad
    Pages 103-146
  9. Back Matter
    Pages 147-153

About this book

Introduction

The appearance of weakly wandering (ww) sets and sequences for ergodic transformations over half a century ago was an unexpected and surprising event. In time it was shown that ww and related sequences reflected significant and deep properties of ergodic transformations that preserve an infinite measure.

This monograph studies in a systematic way the role of ww and related sequences in the classification of ergodic transformations preserving an infinite measure. Connections of these sequences to additive number theory and tilings of the integers are also discussed. The material presented is self-contained and accessible to graduate students. A basic knowledge of measure theory is adequate for the reader.

Keywords

Direct sum decompositions of N and Z Infinite ergodic transformations Invariant measures for ergodic transformations Recurrent and dissipative sequences Weakly wandering and exhaustive weakly wandering sequences

Authors and affiliations

  • Stanley Eigen
    • 1
  • Arshag Hajian
    • 2
  • Yuji Ito
    • 3
  • Vidhu Prasad
    • 4
  1. 1.Department of MathematicsNortheastern UniversityBostonUSA
  2. 2.Department of MathematicsNortheastern UniversityBostonUSA
  3. 3.Department of MathematicsKeio UniversityYokohamaJapan
  4. 4.Department of Mathematical SciencesUniversity of Massachusetts LowellLowellUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-4-431-55108-9
  • Copyright Information Springer Japan 2014
  • Publisher Name Springer, Tokyo
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-4-431-55107-2
  • Online ISBN 978-4-431-55108-9
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site
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