Vitaly Bergelson 
Ergodic IP Polynomial Szemeredi Theorem [PDF ebook] 

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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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Format PDF ● Pages 106 ● ISBN 9781470402860 ● Maison d’édition American Mathematical Society ● Téléchargeable 3 fois ● Devise EUR ● ID 6612892 ● Protection contre la copie Adobe DRM
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