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.
| Original language | English |
|---|---|
| Pages (from-to) | 117-132 |
| Number of pages | 16 |
| Journal | Bulletin of the Polish Academy of Sciences, Mathematics |
| Volume | 68 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2020 |
Bibliographical note
Publisher Copyright:© Instytut Matematyczny PAN, 2020.
Keywords
- ergodic measure
- generic point
- measure-preserving system
- semicontinuous partition
- semisimple system
- strictly uniform system
- topological dynamical system
- uniform system