Journal d’Analyse Mathématique

, Volume 86, Issue 1, pp 183–220 | Cite as

An odd Furstenberg-Szemerédi theorem and quasi-affine systems

Article

Abstract

We prove a version of Furstenberg’s ergodic theorem with restrictions on return times. More specifically, for a measure preserving system (X, B, μ,T), integers 0 ≤j <k, andEX with μ(E) > 0, we show that there existsn ≡ j (modk) with ώ(ET-nE ∩T-2nE ∩T-3nE) > 0, so long asTk is ergodic. This result requires a deeper understanding of the limit of some nonconventional ergodic averages and the introduction of a new class of systems, the ‘Quasi-Affine Systems’.

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Copyright information

© Hebrew University of Jerusalem 2002

Authors and Affiliations

  1. 1.Equipe d’analyse et de mathématiques appliquéesUniverité de Marne la ValléeMarne la Vallée CedexFrance
  2. 2.Department of MathematicsThe Ohio State UniversityColumbusUSA

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