When all points are generic for ergodic measures
Dynamical Systems
2021-01-14 v1
Abstract
We establish connections between several properties of topological dynamical systems, such as: - every point is generic for an ergodic measure, - the map sending points to the measures they generate is continuous, - the system splits into uniquely (alternatively, strictly) ergodic subsystems, - the map sending ergodic measures to their topological supports is continuous, - the Cesaro means of every continuous function converge uniformly.
Cite
@article{arxiv.2101.04967,
title = {When all points are generic for ergodic measures},
author = {Tomasz Downarowicz and Benjamin Weiss},
journal= {arXiv preprint arXiv:2101.04967},
year = {2021}
}
Comments
13 pages, 6 figures