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Mathematical Notes

, Volume 104, Issue 5–6, pp 900–904 | Cite as

Thouvenot’s Isomorphism Problem for Tensor Powers of Ergodic Flows

  • V. V. Ryzhikov
Article
  • 12 Downloads

Abstract

Let S and T be automorphisms of a probability space whose powers SS and TT isomorphic. Are the automorphisms S and T isomorphičThis 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 StSt and TtTt are isomorphic, then so are the flows St and Tt, 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 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.LomonosovMoscow State UniversityMoscowRussia

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