When all points are generic for ergodic measures
Volume 68 / 2020
Bulletin Polish Acad. Sci. Math. 68 (2020), 117-132
MSC: Primary 37B05, 37B20; Secondary 37A25.
DOI: 10.4064/ba210113-15-1
Published online: 25 January 2021
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 Cesàro means of every continuous function converge uniformly.
