|
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
 Full text:
PDF file (487 kB)
References:
PDF file
HTML file
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
\Bibitem{Bas13}
\by A.~I.~Bashtanov
\paper Generic Mixing Transformations Are Rank~$1$
\jour Mat. Zametki
\yr 2013
\vol 93
\issue 2
\pages 163--171
\mathnet{http://mi.mathnet.ru/mz10157}
\crossref{https://doi.org/10.4213/mzm10157}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3205956}
\zmath{https://zbmath.org/?q=an:06158177}
\elib{http://elibrary.ru/item.asp?id=20731671}
\transl
\jour Math. Notes
\yr 2013
\vol 93
\issue 2
\pages 209--216
\crossref{https://doi.org/10.1134/S0001434613010227}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000315582900022}
\elib{http://elibrary.ru/item.asp?id=20431926}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84874566252}
Linking options:
http://mi.mathnet.ru/eng/mz10157https://doi.org/10.4213/mzm10157 http://mi.mathnet.ru/eng/mz/v93/i2/p163
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
-
I. Yaroslavtsev, “On the Asymmetry of the Past and the Future of the Ergodic $\mathbb{Z}$-Action”, Math. Notes, 95:3 (2014), 438–440
 -
V. V. Ryzhikov, “Ergodic homoclinic groups, Sidon constructions and Poisson suspensions”, Trans. Moscow Math. Soc., 75 (2014), 77–85
-
Bashtanov A.I., “Conjugacy Classes Are Dense in the Space of Mixing $\mathbb{Z}^d$-Actions”, Math. Notes, 99:1-2 (2016), 9–23
-
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
-
V. V. Ryzhikov, “Thouvenot's Isomorphism Problem for Tensor Powers of Ergodic Flows”, Math. Notes, 104:6 (2018), 900–904
|
| Number of views: |
| This page: | 420 | | Full text: | 57 | | References: | 47 | | First page: | 37 |
|
Terms of Use