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
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.
PDF file (1299 kB)
Russian Academy of Sciences. Izvestiya Mathematics, 1994, 42:1, 91–114
MSC: Primary 28D10, 28D05; Secondary 58F17
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
\paper Joinings, intertwining operators, factors, and mixing properties of dynamical systems
\jour Izv. RAN. Ser. Mat.
\jour Russian Acad. Sci. Izv. Math.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
V. V. Ryzhikov, “Skew products and multiple mixing of dynamical systems”, Russian Math. Surveys, 49:2 (1994), 170–171
V. V. Ryzhikov, “Intertwinings of tensor products, and the stochastic centralizer of dynamical systems”, Sb. Math., 188:2 (1997), 237–263
E. H. Abdalaoui, “On the spectrum of α-rigid maps”, J Dyn Control Syst, 2009
MARIUSZ LEMAŃCZYK, FRANÇOIS PARREAU, “Lifting mixing properties by Rokhlin cocycles”, Ergod. Th. Dynam. Sys, 2011, 1
YOUNGHWAN SON, “Joint ergodicity of actions of an abelian group”, Ergod. Th. Dynam. Sys, 2013, 1
Krzysztof Frączek, Joanna Kułaga-Przymus, Mariusz Lemańczyk, “Non-reversibility and self-joinings of higher orders for ergodic flows”, JAMA, 122:1 (2014), 163
|Number of views:|