Möbius disjointness for models of an ergodic system and beyond

Abstract : We give a necessary and sufficient condition (called the strong MOMO property) for a uniquely ergodic model of an ergodic measure-preserving system to have all uniquely ergodic models of the system Möbius disjoint. It follows that all uniquely ergodic models of: ergodic unipotent diffeomorphisms on nil-manifolds, discrete spectrum automorphisms, systems given by some substitutions of constant length (including the classical Thue-Morse and Rudin-Shapiro substitutions), systems determined by Kakutani sequences are Möbius disjoint. We also discuss the absence of the strong MOMO property in positive entropy systems.
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Contributor : Thierry de La Rue <>
Submitted on : Monday, April 24, 2017 - 10:44:39 AM
Last modification on : Monday, March 4, 2019 - 2:04:22 PM

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  • HAL Id : hal-01512648, version 1
  • ARXIV : 1704.03506

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El Houcein El Abdalaoui, Joanna Kulaga-Przymus, Mariusz Lemanczyk, Thierry de La Rue. Möbius disjointness for models of an ergodic system and beyond. Israël Journal of Mathematics, The Hebrew University Magnes Press, 2018, 228 (2), pp.707-751. ⟨hal-01512648⟩

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