Birkhoff attractors for dissipative symplectic billiards
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918142208376832 |
|---|---|
| author | Baracco, Luca Bernardi, Olga Florio, Anna Nardi, Alessandra |
| author_facet | Baracco, Luca Bernardi, Olga Florio, Anna Nardi, Alessandra |
| contents | The aim of the present paper is to propose and study a dissipative variant of symplectic billiards within planar strictly convex domains. The associated billiard map is dissipative, thus it admits a compact invariant set, the so-called Birkhoff attractor. Its complexity depends on the rate of the dissipation as well as on the geometry of the billiard table. We prove that (a) for strong dissipation, the Birkhoff attractor is a normally contracted graph over the zero section; (b) for mild dissipation, the Birkhoff attractor within a centrally symmetric domain is an indecomposable continuum whose restricted dynamics has positive topological entropy. We compare these results with the case of dissipative Birkhoff billiards, studied in a paper by Bernardi-Florio-Leguil |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13086 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Birkhoff attractors for dissipative symplectic billiards Baracco, Luca Bernardi, Olga Florio, Anna Nardi, Alessandra Dynamical Systems 37C70, 37G35, 37E40 The aim of the present paper is to propose and study a dissipative variant of symplectic billiards within planar strictly convex domains. The associated billiard map is dissipative, thus it admits a compact invariant set, the so-called Birkhoff attractor. Its complexity depends on the rate of the dissipation as well as on the geometry of the billiard table. We prove that (a) for strong dissipation, the Birkhoff attractor is a normally contracted graph over the zero section; (b) for mild dissipation, the Birkhoff attractor within a centrally symmetric domain is an indecomposable continuum whose restricted dynamics has positive topological entropy. We compare these results with the case of dissipative Birkhoff billiards, studied in a paper by Bernardi-Florio-Leguil |
| title | Birkhoff attractors for dissipative symplectic billiards |
| topic | Dynamical Systems 37C70, 37G35, 37E40 |
| url | https://arxiv.org/abs/2509.13086 |