An ergodic system is dominant exactly when it has positive entropy

Tim Austin; Eli Glasner; Jean Paul Thouvenot; Benjamin Weiss

doi:10.1017/etds.2022.69

An ergodic system is dominant exactly when it has positive entropy

Tim Austin, Eli Glasner, Jean Paul Thouvenot, Benjamin Weiss

Einstein Institute of Mathematics

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

2 Scopus citations

Abstract

An ergodic dynamical system is called dominant if it is isomorphic to a generic extension of itself. It was shown by Glasner et al [On some generic classes of ergodic measure preserving transformations. Trans. Moscow Math. Soc. 82(1) (2021), 15-36] that Bernoulli systems with finite entropy are dominant. In this work, we show first that every ergodic system with positive entropy is dominant, and then that if has zero entropy, then it is not dominant.

Original language	English
Pages (from-to)	3216-3230
Number of pages	15
Journal	Ergodic Theory and Dynamical Systems
Volume	43
Issue number	10
DOIs	https://doi.org/10.1017/etds.2022.69
State	Published - 4 Oct 2023

Bibliographical note

Publisher Copyright:
© 2022 The Author(s). Published by Cambridge University Press.

Keywords

Bernoulli systems
dominant systems
generic properties
relative Bernoulli
very weak Bernoulli

Access to Document

10.1017/etds.2022.69

Cite this

@article{07b7bf2f9b6f4b0aa267a97fc1deaf01,

title = "An ergodic system is dominant exactly when it has positive entropy",

abstract = "An ergodic dynamical system is called dominant if it is isomorphic to a generic extension of itself. It was shown by Glasner et al [On some generic classes of ergodic measure preserving transformations. Trans. Moscow Math. Soc. 82(1) (2021), 15-36] that Bernoulli systems with finite entropy are dominant. In this work, we show first that every ergodic system with positive entropy is dominant, and then that if has zero entropy, then it is not dominant.",

keywords = "Bernoulli systems, dominant systems, generic properties, relative Bernoulli, very weak Bernoulli",

author = "Tim Austin and Eli Glasner and Thouvenot, {Jean Paul} and Benjamin Weiss",

note = "Publisher Copyright: {\textcopyright} 2022 The Author(s). Published by Cambridge University Press.",

year = "2023",

month = oct,

day = "4",

doi = "10.1017/etds.2022.69",

language = "אנגלית",

volume = "43",

pages = "3216--3230",

journal = "Ergodic Theory and Dynamical Systems",

issn = "0143-3857",

publisher = "Cambridge University Press",

number = "10",

}

TY - JOUR

T1 - An ergodic system is dominant exactly when it has positive entropy

AU - Austin, Tim

AU - Glasner, Eli

AU - Thouvenot, Jean Paul

AU - Weiss, Benjamin

PY - 2023/10/4

Y1 - 2023/10/4

N2 - An ergodic dynamical system is called dominant if it is isomorphic to a generic extension of itself. It was shown by Glasner et al [On some generic classes of ergodic measure preserving transformations. Trans. Moscow Math. Soc. 82(1) (2021), 15-36] that Bernoulli systems with finite entropy are dominant. In this work, we show first that every ergodic system with positive entropy is dominant, and then that if has zero entropy, then it is not dominant.

AB - An ergodic dynamical system is called dominant if it is isomorphic to a generic extension of itself. It was shown by Glasner et al [On some generic classes of ergodic measure preserving transformations. Trans. Moscow Math. Soc. 82(1) (2021), 15-36] that Bernoulli systems with finite entropy are dominant. In this work, we show first that every ergodic system with positive entropy is dominant, and then that if has zero entropy, then it is not dominant.

KW - Bernoulli systems

KW - dominant systems

KW - generic properties

KW - relative Bernoulli

KW - very weak Bernoulli

UR - http://www.scopus.com/inward/record.url?scp=85171183105&partnerID=8YFLogxK

U2 - 10.1017/etds.2022.69

DO - 10.1017/etds.2022.69

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85171183105

SN - 0143-3857

VL - 43

SP - 3216

EP - 3230

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 10

ER -

An ergodic system is dominant exactly when it has positive entropy

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this