Some remarks about self-products and entropy

Michael Hochman

doi:10.1017/etds.2024.77

Some remarks about self-products and entropy

Michael Hochman^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

1 Scopus citations

Abstract

Let (X,B,μ,T) be a probability-preserving system with X compact and T a homeomorphism. We show that if every point in X × X is two-sided recurrent, then h_μ(T)=0, resolving a problem of Benjamin Weiss, and that if h_μ(T)= ∞, then every full-measure set in X contains mean-asymptotic pairs (that is, the associated process is not tight), resolving a problem of Ornstein and Weiss.

Original language	English
Pages (from-to)	2183-2193
Number of pages	11
Journal	Ergodic Theory and Dynamical Systems
Volume	45
Issue number	7
DOIs	https://doi.org/10.1017/etds.2024.77
State	Published - 1 Jul 2025

Bibliographical note

Publisher Copyright:
© The Author(s), 2024.

Keywords

entropy
mean asymptotic pairs
tight processes
topological recurrence

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10.1017/etds.2024.77

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KW - entropy

KW - mean asymptotic pairs

KW - tight processes

KW - topological recurrence

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ER -

Some remarks about self-products and entropy

Abstract

Bibliographical note

Keywords

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