On some generic classes of ergodic measure preserving transformations

Author:

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

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

Publisher

American Mathematical Society (AMS)

Subject

Mathematics (miscellaneous)

Reference46 articles.

1. Skew products of Bernoulli shifts with rotations;Adler, R. L.;Israel J. Math.,1972

2. The generic automorphism of a Lebesgue space conjugate to a 𝐺-extension for any finite abelian group 𝐺;Ageev, O. N.;Dokl. Akad. Nauk,2000

3. On the genericity of some nonasymptotic dynamic properties;Ageev, O. N.;Uspekhi Mat. Nauk,2003

4. A typical dynamical system is not simple or semisimple;Ageev, O. N.;Ergodic Theory Dynam. Systems,2003

5. Measure concentration and the weak Pinsker property;Austin, Tim;Publ. Math. Inst. Hautes \'{E}tudes Sci.,2018

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Zero entropy actions of amenable groups are not dominant;Ergodic Theory and Dynamical Systems;2023-03-06

2. Generic extensions of ergodic systems;Sbornik: Mathematics;2023

3. Generic extensions of ergodic systems;Математический сборник;2023

4. An ergodic system is dominant exactly when it has positive entropy;Ergodic Theory and Dynamical Systems;2022-11-04

5. Compact families and typical entropy invariants of measure-preserving actions;Transactions of the Moscow Mathematical Society;2022-03-15

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3