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Mat. Sb., 2006, Volume 197, Number 11, Pages 143–158 (Mi msb1114)  

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

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.

DOI: https://doi.org/10.4213/sm1114

Full text: PDF file (525 kB)
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English version:
Sbornik: Mathematics, 2006, 197:11, 1697–1712

Bibliographic databases:

UDC: 517.938
MSC: Primary 37A05; Secondary 37A45
Received: 19.07.2005 and 25.05.2006

Citation: I. D. Shkredov, “Dynamical systems with low recurrence rate”, Mat. Sb., 197:11 (2006), 143–158; Sb. Math., 197:11 (2006), 1697–1712

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. D. Shkredov, “Szemerédi's theorem and problems on arithmetic progressions”, Russian Math. Surveys, 61:6 (2006), 1101–1166  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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