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An Ergodic IP Polynomial Szemerédi Theorem
 
Vitaly Bergelson Ohio State University, Columbus, OH
Randall McCutcheon University of Maryland, College Park, MD
An Ergodic IP Polynomial Szemeredi Theorem
eBook ISBN:  978-1-4704-0286-0
Product Code:  MEMO/146/695.E
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $31.20
An Ergodic IP Polynomial Szemeredi Theorem
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An Ergodic IP Polynomial Szemerédi Theorem
Vitaly Bergelson Ohio State University, Columbus, OH
Randall McCutcheon University of Maryland, College Park, MD
eBook ISBN:  978-1-4704-0286-0
Product Code:  MEMO/146/695.E
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $31.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1462000; 106 pp
    MSC: Primary 28; Secondary 05; 11

    We prove a polynomial multiple recurrence theorem for finitely many commuting measure preserving transformations of a probability space, extending a polynomial Szemerédi theorem appearing in [BL1]. The linear case is a consequence of an ergodic IP-Szemerédi theorem of Furstenberg and Katznelson ([FK2]). Several applications to the fine structure of recurrence in ergodic theory are given, some of which involve weakly mixing systems, for which we also prove a multiparameter weakly mixing polynomial ergodic theorem. The techniques and apparatus employed include a polynomialization of an IP structure theory developed in [FK2], an extension of Hindman's theorem due to Milliken and Taylor ([M], [T]), a polynomial version of the Hales-Jewett coloring theorem ([BL2]), and a theorem concerning limits of polynomially generated IP-systems of unitary operators ([BFM]).

    Readership

    Researchers interested in measure-preserving transformations, partitions of integers, Ramsey theory, sequences and sets.

  • Table of Contents
     
     
    • Chapters
    • 0. Introduction
    • 1. Formulation of main theorem
    • 2. Preliminaries
    • 3. Primitive extensions
    • 4. Relative polynomial mixing
    • 5. Completion of the proof
    • 6. Measure-theoretic applications
    • 7. Combinatorial applications
    • 8. For future investigation
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1462000; 106 pp
MSC: Primary 28; Secondary 05; 11

We prove a polynomial multiple recurrence theorem for finitely many commuting measure preserving transformations of a probability space, extending a polynomial Szemerédi theorem appearing in [BL1]. The linear case is a consequence of an ergodic IP-Szemerédi theorem of Furstenberg and Katznelson ([FK2]). Several applications to the fine structure of recurrence in ergodic theory are given, some of which involve weakly mixing systems, for which we also prove a multiparameter weakly mixing polynomial ergodic theorem. The techniques and apparatus employed include a polynomialization of an IP structure theory developed in [FK2], an extension of Hindman's theorem due to Milliken and Taylor ([M], [T]), a polynomial version of the Hales-Jewett coloring theorem ([BL2]), and a theorem concerning limits of polynomially generated IP-systems of unitary operators ([BFM]).

Readership

Researchers interested in measure-preserving transformations, partitions of integers, Ramsey theory, sequences and sets.

  • Chapters
  • 0. Introduction
  • 1. Formulation of main theorem
  • 2. Preliminaries
  • 3. Primitive extensions
  • 4. Relative polynomial mixing
  • 5. Completion of the proof
  • 6. Measure-theoretic applications
  • 7. Combinatorial applications
  • 8. For future investigation
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.