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
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.
PDF file (387 kB)
Sbornik: Mathematics, 1997, 188:2, 237–263
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
\paper Intertwinings of tensor products, and the~stochastic centralizer of dynamical systems
\jour Mat. Sb.
\jour Sb. Math.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
V. V. Ryzhikov, J. Thouvenot, “Disjointness, Divisibility, and Quasi-Simplicity of Measure-Preserving Actions”, Funct. Anal. Appl., 40:3 (2006), 237–240
Danilenko A.I., Ryzhikov V.V., “On self-similarities of ergodic flows”, Proc London Math Soc, 104:3 (2012), 431–454
Kulaga J., “On the Self-Similarity Problem for Smooth Flows on Orientable Surfaces”, Ergod. Theory Dyn. Syst., 32:Part 5 (2012), 1615–1660
V. V. Ryzhikov, “Bounded ergodic constructions, disjointness, and weak limits of powers”, Trans. Moscow Math. Soc., 74 (2013), 165–171
Fraczek K., Kulaga J., Lemanczyk M., “On the Self-Similarity Problem for Gaussian-Kronecker Flows”, Proc. Amer. Math. Soc., 141:12 (2013), 4275–4291
|Number of views:|