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This article is cited in 5 scientific papers (total in 5 papers)
Generic Mixing Transformations Are Rank $1$
A. I. Bashtanov
M. V. Lomonosov Moscow State University
Abstract:
In 2007, S. V. Tikhonov introduced a complete metric on the space of mixing transformations. This metric generates a topology called the leash topology. Tikhonov posed the following problem: what conditions should be satisfied by a mixing transformation $T$ for its conjugacy class to be dense in the space of mixing transformations equipped with the leash topology. We show the conjugacy class to be dense for every mixing transformation $T$. As a corollary, we find that a generic mixing transformation is rank $1$.
Keywords:
mixing transformation, probability space, conjugacy class, Tikhonov metric, leash topology.
DOI:
https://doi.org/10.4213/mzm10157
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English version:
Mathematical Notes, 2013, 93:2, 209–216
Bibliographic databases:
    
UDC:
517.987.5+938.5
Received: 13.06.2012
Revised: 09.10.2012
Citation:
A. I. Bashtanov, “Generic Mixing Transformations Are Rank $1$”, Mat. Zametki, 93:2 (2013), 163–171; Math. Notes, 93:2 (2013), 209–216
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/mz10157https://doi.org/10.4213/mzm10157 http://mi.mathnet.ru/eng/mz/v93/i2/p163
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Bashtanov A.I., “Conjugacy Classes Are Dense in the Space of Mixing $\mathbb{Z}^d$-Actions”, Math. Notes, 99:1-2 (2016), 9–23
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Y. Gutman, W. Huang, S. Shao, X. D. Ye, “Almost sure convergence of the multiple ergodic average for certain weakly mixing systems”, Acta. Math. Sin.-English Ser., 34:1 (2018), 79–90
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V. V. Ryzhikov, “Thouvenot's Isomorphism Problem for Tensor Powers of Ergodic Flows”, Math. Notes, 104:6 (2018), 900–904
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