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Izv. RAN. Ser. Mat., 1993, Volume 57, Issue 1, Pages 102–128 (Mi izv889)  

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

Joinings, intertwining operators, factors, and mixing properties of dynamical systems

V. V. Ryzhikov


Abstract: This paper is mostly devoted to the following problem. If the Markov (stochastic) centralizer of a measure-preserving action $\Psi$ is known, what can be said about the Markov centralizer of the action $\Psi\otimes\Psi$? For a mixing flow with minimal Markov centralizer the author proves the triviality of the Markov centralizer of a Cartesian power of it, from which it follows that this flow possesses mixing of arbitrary multiplicity. For actions of the groups $\mathbf Z^n$ the analogous assertion holds if their tensor product with themselves does not possess three pairwise independent factors. In particular, this is true for actions of $\mathbf Z^n$ admitting a partial approximation and possessing mixing of multiplicity 2.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1994, 42:1, 91–114

Bibliographic databases:

UDC: 512.54
MSC: Primary 28D10, 28D05; Secondary 58F17
Received: 17.07.1991

Citation: V. V. Ryzhikov, “Joinings, intertwining operators, factors, and mixing properties of dynamical systems”, Izv. RAN. Ser. Mat., 57:1 (1993), 102–128; Russian Acad. Sci. Izv. Math., 42:1 (1994), 91–114

Citation in format AMSBIB
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\by V.~V.~Ryzhikov
\paper Joinings, intertwining operators, factors, and mixing properties of dynamical systems
\jour Izv. RAN. Ser. Mat.
\yr 1993
\vol 57
\issue 1
\pages 102--128
\mathnet{http://mi.mathnet.ru/izv889}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1220583}
\zmath{https://zbmath.org/?q=an:0853.28010}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1994IzMat..42...91R}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1994
\vol 42
\issue 1
\pages 91--114
\crossref{https://doi.org/10.1070/IM1994v042n01ABEH001535}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994NH32100005}


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    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:
    1. V. V. Ryzhikov, “Skew products and multiple mixing of dynamical systems”, Russian Math. Surveys, 49:2 (1994), 170–171  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. V. V. Ryzhikov, “Intertwinings of tensor products, and the stochastic centralizer of dynamical systems”, Sb. Math., 188:2 (1997), 237–263  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. E. H. Abdalaoui, “On the spectrum of α-rigid maps”, J Dyn Control Syst, 2009  crossref  mathscinet  isi
    4. MARIUSZ LEMAŃCZYK, FRANÇOIS PARREAU, “Lifting mixing properties by Rokhlin cocycles”, Ergod. Th. Dynam. Sys, 2011, 1  crossref
    5. YOUNGHWAN SON, “Joint ergodicity of actions of an abelian group”, Ergod. Th. Dynam. Sys, 2013, 1  crossref
    6. Krzysztof Frączek, Joanna Kułaga-Przymus, Mariusz Lemańczyk, “Non-reversibility and self-joinings of higher orders for ergodic flows”, JAMA, 122:1 (2014), 163  crossref
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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