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Mixing Sets for Rigid Transformations

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Abstract

It is shown that, for any infinite set \(M\subset\mathbb N\) of density zero, there exists a rigid measure-preserving transformation of a probability space which is mixing along \(M\). As examples, Gaussian actions and Poisson suspensions over infinite rank-one constructions are considered. Analogues of the obtained result for group actions and a method not using Gaussian and Poisson suspensions are also discussed.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    V. V. Ryzhikov

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  1. V. V. Ryzhikov
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Correspondence to V. V. Ryzhikov.

Additional information

Translated from Matematicheskie Zametki, 2021, Vol. 110, pp. 576–583 https://doi.org/10.4213/mzm13128.

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Ryzhikov, V.V. Mixing Sets for Rigid Transformations. Math Notes 110, 565–570 (2021). https://doi.org/10.1134/S0001434621090261

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  • DOI: https://doi.org/10.1134/S0001434621090261

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