A note on logarithmic mean equicontinuity
arXiv:2502.04610 · doi:10.1007/s10884-025-10457-z
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 Cesà ro 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.
17 pages, to appear in J. Dynam. Differential Equations