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Mat. Zametki, 2018, Volume 104, Issue 6, Pages 912–917 (Mi mz11987)  

Thouvenot's Isomorphism Problem for Tensor Powers of Ergodic Flows

V. V. Ryzhikov

Lomonosov Moscow State University

Abstract: Let $S$ and $T$ be automorphisms of a probability space whose powers $S \otimes S$ and $T \otimes T$ isomorphic. Are the automorphisms $S$ and $T$ isomorphic? This question of Thouvenot is well known in ergodic theory. We answer this question and generalize a result of Kulaga concerning isomorphism in the case of flows. We show that if weakly mixing flows $S_t \otimes S_t$ and $T_t \otimes T_t$ are isomorphic, then so are the flows $S_t$ and $T_t$, provided that one of them has a weak integral limit.

Keywords: flow with invariant measure, weak closure, tensor power of a dynamical system, metric isomorphism.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-6222.2018.1
This work was supported by the program “Leading Scientific Schools” under grant NSh-6222.2018.1.


DOI: https://doi.org/10.4213/mzm11987

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English version:
Mathematical Notes, 2018, 104:6, 900–904

Bibliographic databases:

Document Type: Article
UDC: 517.9
Received: 01.03.2018
Revised: 17.03.2018

Citation: V. V. Ryzhikov, “Thouvenot's Isomorphism Problem for Tensor Powers of Ergodic Flows”, Mat. Zametki, 104:6 (2018), 912–917; Math. Notes, 104:6 (2018), 900–904

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