The mean orbital pseudo-metric and the space of invariant measures
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914100100988928 |
|---|---|
| author | Li, Jian Xiao, Yuanfen |
| author_facet | Li, Jian Xiao, Yuanfen |
| contents | We study the mean orbital pseudo-metric for Polish dynamical systems and its connections with properties of the space of invariant measures. We give equivalent conditions for when the set of invariant measures generated by periodic points is dense in the set of ergodic measures and the space of invariant measures. We also introduce the concept of asymptotic orbital average shadowing property and show that it implies that every non-empty compact connected subset of the space of invariant measures has a generic point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_07208 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The mean orbital pseudo-metric and the space of invariant measures Li, Jian Xiao, Yuanfen Dynamical Systems 37B65, 37B05 We study the mean orbital pseudo-metric for Polish dynamical systems and its connections with properties of the space of invariant measures. We give equivalent conditions for when the set of invariant measures generated by periodic points is dense in the set of ergodic measures and the space of invariant measures. We also introduce the concept of asymptotic orbital average shadowing property and show that it implies that every non-empty compact connected subset of the space of invariant measures has a generic point. |
| title | The mean orbital pseudo-metric and the space of invariant measures |
| topic | Dynamical Systems 37B65, 37B05 |
| url | https://arxiv.org/abs/2311.07208 |