Some remarks about self-products and entropy

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Abstract

Let (X, β, 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 hμ (T)=0, resolving a problem of Benjamin Weiss, and that if hμ (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 languageEnglish
JournalErgodic Theory and Dynamical Systems
DOIs
StateAccepted/In press - 2024

Keywords

  • entropy
  • mean asymptotic pairs
  • tight processes
  • topological recurrence

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

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