Quasi-Similarity, Entropy and Disjointness of Ergodic Actions

Авторы: Ryzhikov V.V., Thouvenot J.P.
Журнал: Functional Analysis and its Applications
Том: 58
Номер: 1
Год издания: 2024
Издательство: Maik Nauka/Interperiodica Publishing
Местоположение издательства: Russian Federation
Первая страница: 91
Последняя страница: 97
DOI: 10.1134/S0016266324010088
Аннотация: We answer a question of Vershik regarding connections between quasi-similarity ofdynamical systems and Kolmogorov entropy. We prove that all Bernoulli actions of a given countably infinite group are quasi-similar to each other. Existence of non-Bernoulli actions in the samequasi-similarity class is an open problem. A notion opposite to quasi-similarity is that of disjointness (or independence) of actions. Pinsker proved that a deterministic action is independent from an action with completely positive entropy. Using joinings, we obtain the following generalization of Pinsker’s theorem: an action with zero P-entropy (an invariant defined by Kirillov and Kushnirenko)and an action with completely positive P-entropy are disjoint.
Добавил в систему: Рыжиков Валерий Валентинович

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