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Sbornik: Mathematics, 2006, Volume 197, Issue 11, Pages 1697–1712
DOI: https://doi.org/10.1070/SM2006v197n11ABEH003818
(Mi sm1114)
 

This article is cited in 1 scientific paper (total in 1 paper)

Dynamical systems with low recurrence rate

I. D. Shkredov

M. V. Lomonosov Moscow State University
References:
Abstract: The question on the recurrence rate of a dynamical system in a metric space of finite Hausdorff measure is considered. For such systems upper bounds for the rate of simple recurrence are due to Boshernitzan and ones for the rate of multiple recurrence to the present author. The subject of the paper are lower bounds for the rate of multiple recurrence. More precisely, an example of a dynamical system (an odometer or a von Neumann transformation) with a low rate of multiple recurrence is constructed. Behrend's theorem on sets containing no arithmetic progressions is used in the proof.
Bibliography: 22 titles.
Received: 19.07.2005 and 25.05.2006
Bibliographic databases:
UDC: 517.938
MSC: Primary 37A05; Secondary 37A45
Language: English
Original paper language: Russian
Citation: I. D. Shkredov, “Dynamical systems with low recurrence rate”, Sb. Math., 197:11 (2006), 1697–1712
Citation in format AMSBIB
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\by I.~D.~Shkredov
\paper Dynamical systems with low recurrence rate
\jour Sb. Math.
\yr 2006
\vol 197
\issue 11
\pages 1697--1712
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  • https://doi.org/10.1070/SM2006v197n11ABEH003818
  • https://www.mathnet.ru/eng/sm/v197/i11/p143
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
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    Abstract page:600
    Russian version PDF:229
    English version PDF:12
    References:50
    First page:3
     
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