Symmetric homoclinic tangles in reversible dynamical systems have positive topological entropy
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916580177215488 |
|---|---|
| author | Homburg, Ale Jan Lamb, Jeroen Turaev, Dmitry |
| author_facet | Homburg, Ale Jan Lamb, Jeroen Turaev, Dmitry |
| contents | We consider reversible vector fields in $\mathbb{R}^{2n}$ such that the set of fixed points of the involutory reversing symmetry is $n$-dimensional. Let such system have a smooth one-parameter family of symmetric periodic orbits which is of saddle type in normal directions. We establish that topological entropy is positive when the stable and unstable manifolds of this family of periodic orbits have a strongly-transverse intersection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_10624 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Symmetric homoclinic tangles in reversible dynamical systems have positive topological entropy Homburg, Ale Jan Lamb, Jeroen Turaev, Dmitry Dynamical Systems 34C37, 37B40 We consider reversible vector fields in $\mathbb{R}^{2n}$ such that the set of fixed points of the involutory reversing symmetry is $n$-dimensional. Let such system have a smooth one-parameter family of symmetric periodic orbits which is of saddle type in normal directions. We establish that topological entropy is positive when the stable and unstable manifolds of this family of periodic orbits have a strongly-transverse intersection. |
| title | Symmetric homoclinic tangles in reversible dynamical systems have positive topological entropy |
| topic | Dynamical Systems 34C37, 37B40 |
| url | https://arxiv.org/abs/2207.10624 |