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Труды Московского математического общества, 2021, том 82, выпуск 1, страницы 19–44
(Mi mmo645)
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Эта публикация цитируется в 6 научных статьях (всего в 6 статьях)
On some generic classes of ergodic measure preserving transformations
E. Glasnera, J.-P. Thouvenotb, B. Weissc a Tel Aviv University
b Paris Sorbonne University
c Hebrew University of Jerusalem
Аннотация:
We answer positively a question of Ryzhikov, namely we show that being a relatively weakly mixing extension is a comeager property in the Polish group of measure preserving transformations. We study some related classes of ergodic transformations and their interrelations. In the second part of the paper we show that for a fixed ergodic $T$ with property $\mathbf{A}$, a generic extension $\widehat{T}$ of $T$ also has the property $\mathbf{A}$. Here $\mathbf{A}$ stands for each of the following properties: (i) having the same entropy as $T$, (ii) Bernoulli, (iii) K, and (iv) loosely Bernoulli. References: 46 entries.
Ключевые слова и фразы:
relative weak mixing, comeager properties, prime dynamical systems, Bernoulli systems, K-systems, loosely Bernoulli systems.
Поступила в редакцию: 09.11.2020 Исправленный вариант: 22.02.2021
Образец цитирования:
E. Glasner, J.-P. Thouvenot, B. Weiss, “On some generic classes of ergodic measure preserving transformations”, Тр. ММО, 82, no. 1, МЦНМО, М., 2021, 19–44; Trans. Moscow Math. Soc., 82 (2021), 15–36
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/mmo645 https://www.mathnet.ru/rus/mmo/v82/i1/p19
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