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Mat. Sb., 1997, Volume 188, Number 2, Pages 67–94 (Mi msb202)  

This article is cited in 5 scientific papers (total in 5 papers)

Intertwinings of tensor products, and the stochastic centralizer of dynamical systems

V. V. Ryzhikov

M. V. Lomonosov Moscow State University

Abstract: A dynamical system is called $\omega$-simple if all its ergodic joinings of the second order (except for $\mu \otimes \mu$) are measures concentrated on the graphs of finite-valued maps commuting with the system, the number of inequivalent graphs of this kind being at most countable. This class of dynamical systems contains, for example, horocycle flows and mixing actions of the group $\mathbb R^n$ with partial cyclic approximation. It is proved in this paper that $\omega$-simple mixing flows have multiple mixing, which is a consequence of results on stochastic intertwinings of flows. Properties of dynamical systems with general time are investigated in this direction, including actions with discrete and non-commutative time. The results obtained depend on the type of system.

DOI: https://doi.org/10.4213/sm202

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English version:
Sbornik: Mathematics, 1997, 188:2, 237–263

Bibliographic databases:

UDC: 517.93
MSC: 28Dxx
Received: 27.11.1995

Citation: V. V. Ryzhikov, “Intertwinings of tensor products, and the stochastic centralizer of dynamical systems”, Mat. Sb., 188:2 (1997), 67–94; Sb. Math., 188:2 (1997), 237–263

Citation in format AMSBIB
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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, J. Thouvenot, “Disjointness, Divisibility, and Quasi-Simplicity of Measure-Preserving Actions”, Funct. Anal. Appl., 40:3 (2006), 237–240  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Danilenko A.I., Ryzhikov V.V., “On self-similarities of ergodic flows”, Proc London Math Soc, 104:3 (2012), 431–454  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    3. Kulaga J., “On the Self-Similarity Problem for Smooth Flows on Orientable Surfaces”, Ergod. Theory Dyn. Syst., 32:Part 5 (2012), 1615–1660  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    4. V. V. Ryzhikov, “Bounded ergodic constructions, disjointness, and weak limits of powers”, Trans. Moscow Math. Soc., 74 (2013), 165–171  mathnet  crossref  mathscinet  zmath  elib
    5. Fraczek K., Kulaga J., Lemanczyk M., “On the Self-Similarity Problem for Gaussian-Kronecker Flows”, Proc. Amer. Math. Soc., 141:12 (2013), 4275–4291  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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