Chaos for foliated spaces and pseudogroups
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912146813616128 |
|---|---|
| author | Lijó, Ramón Barral |
| author_facet | Lijó, Ramón Barral |
| contents | We generalize "sensitivity to initial conditions" to foliated spaces and pseudogroups, offering a definition of Devaney chaos in this setting. In contrast to the case of group actions, where sensitivity follows from the other two conditions of Devaney chaos, we show that this is true only for compact foliated spaces, exhibiting a counterexample in the non-compact case. Finally, we obtain an analogue of the Auslander-Yorke dichotomy for compact foliated spaces and compactly generated pseudogroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_09983 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Chaos for foliated spaces and pseudogroups Lijó, Ramón Barral Dynamical Systems 37B02 37B05 We generalize "sensitivity to initial conditions" to foliated spaces and pseudogroups, offering a definition of Devaney chaos in this setting. In contrast to the case of group actions, where sensitivity follows from the other two conditions of Devaney chaos, we show that this is true only for compact foliated spaces, exhibiting a counterexample in the non-compact case. Finally, we obtain an analogue of the Auslander-Yorke dichotomy for compact foliated spaces and compactly generated pseudogroups. |
| title | Chaos for foliated spaces and pseudogroups |
| topic | Dynamical Systems 37B02 37B05 |
| url | https://arxiv.org/abs/2202.09983 |