Dynamical systems with low recurrence rate

DOI10.1070/SM2006V197N11ABEH003818zbMATH Open1152.37005arXivmath/0507345MaRDI QIDQ3533491

Ilya D. Shkredov

Publication date: 23 October 2008

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Abstract: Using a result of Behrend concerning sets without arithmetic progressions, we construct some examples of dynamical systems with slow time of multiple recurrence. Our theorem is a quatitative analog of Furstenberg's Correspondence Principle.

Full work available at URL: https://arxiv.org/abs/math/0507345

zbMATH Keywords

lower boundsPoincaré recurrencemultiple recurrence

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Related Items (1)

Multiple recurrence and nilsequences (with an appendix by Imre Ruzsa)

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