Year: 2024
Type: article
Abstract: Let $(X,\mathcal {B},\mu ,T)$ be a probability-preserving system with X compact and T a homeomorphism. We show that if every point in $X\times X$ is two-sided recurrent, then $h_{\mu }(T)=0$ , resolving a problem of Benjamin Weiss, and that if $h_{\mu }(T)=\infty $ , 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.
DOI: 10.1017/etds.2024.77
Author: MICHAEL HOCHMAN
Institution: Hebrew University of Jerusalem
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,450
Funder: Israel Science Foundation
Award: G7395179634
OpenAlex ID: W4405826028