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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
English version PDF (313 kB) Citations (1)
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DOI: https://doi.org/10.1070/SM2006v197n11ABEH003818
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
Russian version:
Matematicheskii Sbornik, 2006, Volume 197, Number 11, Pages 143–158
DOI: https://doi.org/10.4213/sm1114
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”, Mat. Sb., 197:11 (2006), 143–158; Sb. Math., 197:11 (2006), 1697–1712
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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