ON SOME GENERIC CLASSES OF ERGODIC MEASURE PRESERVING TRANSFORMATIONS

E. Glasner; J. P. Thouvenot; B. Weiss

doi:10.1090/mosc/312

ON SOME GENERIC CLASSES OF ERGODIC MEASURE PRESERVING TRANSFORMATIONS

E. Glasner, J. P. Thouvenot, B. Weiss

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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 A, a generic extension ̂T of T also has property A. Here A stands for each of the following properties: (i) having the same entropy as T, (ii) Bernoulli, (iii) K, and (iv) loosely Bernoulli.

Original language	English
Pages (from-to)	15-36
Number of pages	22
Journal	Transactions of the Moscow Mathematical Society
Volume	82
DOIs	https://doi.org/10.1090/mosc/312
State	Published - 2021

Bibliographical note

Publisher Copyright:
© 2021 E. Glasner, J.-P. Thouvenot, B. Weiss.

Keywords

Bernoulli systems
comeager properties
K-systems
loosely Bernoulli systems
prime dynamical systems
Relative weak mixing

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10.1090/mosc/312

Cite this

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abstract = "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 A, a generic extension{\^ }T of T also has property A. Here A stands for each of the following properties: (i) having the same entropy as T, (ii) Bernoulli, (iii) K, and (iv) loosely Bernoulli.",

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AU - Thouvenot, J. P.

AU - Weiss, B.

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AB - 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 A, a generic extension ̂T of T also has property A. Here A stands for each of the following properties: (i) having the same entropy as T, (ii) Bernoulli, (iii) K, and (iv) loosely Bernoulli.

KW - Bernoulli systems

KW - comeager properties

KW - K-systems

KW - loosely Bernoulli systems

KW - prime dynamical systems

KW - Relative weak mixing

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JO - Transactions of the Moscow Mathematical Society

JF - Transactions of the Moscow Mathematical Society

ER -

ON SOME GENERIC CLASSES OF ERGODIC MEASURE PRESERVING TRANSFORMATIONS

Abstract

Bibliographical note

Keywords

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