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Trudy Moskovskogo Matematicheskogo Obshchestva, 2021, Volume 82, Issue 1, Pages 19–44 (Mi mmo645)  

This article is cited in 6 scientific papers (total in 6 papers)

On some generic classes of ergodic measure preserving transformations

E. Glasnera, J.-P. Thouvenotb, B. Weissc

a Tel Aviv University
b Paris Sorbonne University
c Hebrew University of Jerusalem
Full-text PDF (266 kB) Citations (6)
References:
Abstract: We answer positively a question of Ryzhikov, namely we show that being a relatively weakly mixing extension is a comeager property in the Polish group of measure preserving transformations. We study some related classes of ergodic transformations and their interrelations. In the second part of the paper we show that for a fixed ergodic T with property A, a generic extension ˆT of T also has the property A. Here A stands for each of the following properties: (i) having the same entropy as T, (ii) Bernoulli, (iii) K, and (iv) loosely Bernoulli. References: 46 entries.
Key words and phrases: relative weak mixing, comeager properties, prime dynamical systems, Bernoulli systems, K-systems, loosely Bernoulli systems.
Received: 09.11.2020
Revised: 22.02.2021
English version:
Transactions of the Moscow Mathematical Society, 2021, Volume 82, Pages 15–36
DOI: https://doi.org/10.1090/mosc/312
Bibliographic databases:
Document Type: Article
UDC: 517.987
Language: English
Citation: E. Glasner, J.-P. Thouvenot, B. Weiss, “On some generic classes of ergodic measure preserving transformations”, Tr. Mosk. Mat. Obs., 82, no. 1, MCCME, M., 2021, 19–44; Trans. Moscow Math. Soc., 82 (2021), 15–36
Citation in format AMSBIB
\Bibitem{GlaThoWei21}
\by E.~Glasner, J.-P.~Thouvenot, B.~Weiss
\paper On some generic classes of ergodic measure preserving transformations
\serial Tr. Mosk. Mat. Obs.
\yr 2021
\vol 82
\issue 1
\pages 19--44
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo645}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2021
\vol 82
\pages 15--36
\crossref{https://doi.org/10.1090/mosc/312}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85127504467}
Linking options:
  • https://www.mathnet.ru/eng/mmo645
  • https://www.mathnet.ru/eng/mmo/v82/i1/p19
  • This publication is cited in the following 6 articles:
    1. ADAM LOTT, “Zero entropy actions of amenable groups are not dominant”, Ergod. Th. Dynam. Sys., 44:2 (2024), 630  crossref
    2. V. V. Ryzhikov, “Self-joinings and generic extensions of ergodic systems”, Funct. Anal. Appl., 57:3 (2023), 236–247  mathnet  crossref  crossref
    3. V. V. Ryzhikov, “Generic extensions of ergodic systems”, Sb. Math., 214:10 (2023), 1442–1457  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. TIM AUSTIN, ELI GLASNER, JEAN-PAUL THOUVENOT, BENJAMIN WEISS, “An ergodic system is dominant exactly when it has positive entropy”, Ergod. Th. Dynam. Sys., 43:10 (2023), 3216  crossref
    5. V. V. Ryzhikov, “Tensor simple spectrum of unitary flows”, Funct. Anal. Appl., 56:4 (2022), 327–330  mathnet  crossref  crossref
    6. V. V. Ryzhikov, “Compact families and typical entropy invariants of measure-preserving actions”, Trans. Moscow Math. Soc., 82 (2021), 117–123  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Trudy Moskovskogo Matematicheskogo Obshchestva
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    Abstract page:129
    Full-text PDF :19
    References:32
    First page:8
     
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