A note on logarithmic mean equicontinuity
Dynamical Systems
2025-09-03 v2
Abstract
We study the set of harmonic limits of empirical measures in topological dynamical systems. We obtain a characterization of unique ergodicity based of logarithmic (harmonic) mean convergence in place of Ces\`aro convergence. We introduce logarithmic mean equicontinuity and show that a topological dynamical system is logarithmically mean equicontinuous if and only if it is mean equicontinuous.
Cite
@article{arxiv.2502.04610,
title = {A note on logarithmic mean equicontinuity},
author = {Dominik Kwietniak and Jian Li and Habibeh Pourmand},
journal= {arXiv preprint arXiv:2502.04610},
year = {2025}
}
Comments
17 pages, to appear in J. Dynam. Differential Equations