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Tr. Mat. Inst. Steklova, 2010, Volume 271, Pages 29–39 (Mi tm3248)  

This article is cited in 2 scientific papers (total in 2 papers)

Property of almost independent images for ergodic transformations without partial rigidity

A. I. Bashtanov

Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia

Abstract: S. V. Tikhonov, in his paper of 2007 devoted to a new metric on the class of mixing transformations, faced the following natural question when studying the properties of such transformations: Does there exist a set $A$ with $\mu(A)=\frac12$ such that the inequality $|\mu(A\cap T^iA)-\mu(A)^2|<\varepsilon$ holds for all $i>0$? V. V. Ryzhikov (2009) obtained the following criterion: For an ergodic transformation $T$, a set $A$ of given measure such that $A$ and its images under $T$ are $\varepsilon$-independent exists if and only if $T$ does not possess the property of partial rigidity. The aim of the present study is to generalize this proposition to the case of multiple $\varepsilon$-independence of images.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 271, 23–33

Bibliographic databases:

UDC: 517.987.5
Received in December 2009

Citation: A. I. Bashtanov, “Property of almost independent images for ergodic transformations without partial rigidity”, Differential equations and topology. II, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Tr. Mat. Inst. Steklova, 271, MAIK Nauka/Interperiodica, Moscow, 2010, 29–39; Proc. Steklov Inst. Math., 271 (2010), 23–33

Citation in format AMSBIB
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\by A.~I.~Bashtanov
\paper Property of almost independent images for ergodic transformations without partial rigidity
\inbook Differential equations and topology.~II
\bookinfo Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin
\serial Tr. Mat. Inst. Steklova
\yr 2010
\vol 271
\pages 29--39
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3248}
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\jour Proc. Steklov Inst. Math.
\yr 2010
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\pages 23--33
\crossref{https://doi.org/10.1134/S0081543810040048}
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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. A. I. Bashtanov, “Generic Mixing Transformations Are Rank $1$”, Math. Notes, 93:2 (2013), 209–216  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Bashtanov A.I., “Conjugacy Classes Are Dense in the Space of Mixing a"Currency Sign (D) -Actions”, Math. Notes, 99:1-2 (2016), 9–23  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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