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

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

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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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
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
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