An Ergodic IP Polynomial Szemeredi Theorem (Memoirs of the American Mathematical Society No. 695)

An Ergodic IP Polynomial Szemeredi Theorem (Memoirs of the American Mathematical Society No. 695)

By: Randall McCutcheon (author), Vitaly Bergelson (author)Paperback

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Description

We prove a polynomial multiple recurrence theorem for finitely many commuting measure preserving transformations of a probability space, extending a polynomial Szemeredi theorem appearing in [BL1]. The linear case is a consequence of an ergodic IP-Szemeredi 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]).

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Contents

Introduction Formulation of main theorem Preliminaries Primitive extensions Relative polynomial mixing Completion of the proof Measure-theoretic applications Combinatorial applications For future investigation Appendix: Multiparameter weakly mixing PET References Index of notation Index.

Product Details

  • publication date: 15/07/2000
  • ISBN13: 9780821826577
  • Format: Paperback
  • Number Of Pages: 106
  • ID: 9780821826577
  • weight: 33
  • ISBN10: 0821826573

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