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 language | English |
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Journal | Ergodic Theory and Dynamical Systems |
DOIs | |
State | Accepted/In press - 2024 |
Keywords
- entropy
- mean asymptotic pairs
- tight processes
- topological recurrence
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics