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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.
Received: 19.07.2005 and 25.05.2006
Citation:
I. D. Shkredov, “Dynamical systems with low recurrence rate”, Sb. Math., 197:11 (2006), 1697–1712
Linking options:
https://www.mathnet.ru/eng/sm1114https://doi.org/10.1070/SM2006v197n11ABEH003818 https://www.mathnet.ru/eng/sm/v197/i11/p143
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Abstract page: | 600 | Russian version PDF: | 229 | English version PDF: | 12 | References: | 50 | First page: | 3 |
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