Weakly Mixing Polygonal Billiards
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916899690905600 |
|---|---|
| author | Chaika, Jon Forni, Giovanni |
| author_facet | Chaika, Jon Forni, Giovanni |
| contents | We prove that there exists a residual set of (non-rational) polygons such the billiard flow is weakly mixing with respect to the Liouville measure (on the unit tangent bundle to the billiard). This follows, via a Baire category argument, from showing that for any translation surface the product of the flows in almost every pair of directions is ergodic with respect to Lebesgue measure. This in turn is proven by showing that for every translation surface the flows in almost every pair of directions do not share non-trivial common eigenvalues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_00890 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Weakly Mixing Polygonal Billiards Chaika, Jon Forni, Giovanni Dynamical Systems Geometric Topology 37A25, 37E35, 30F60, 32G15 We prove that there exists a residual set of (non-rational) polygons such the billiard flow is weakly mixing with respect to the Liouville measure (on the unit tangent bundle to the billiard). This follows, via a Baire category argument, from showing that for any translation surface the product of the flows in almost every pair of directions is ergodic with respect to Lebesgue measure. This in turn is proven by showing that for every translation surface the flows in almost every pair of directions do not share non-trivial common eigenvalues. |
| title | Weakly Mixing Polygonal Billiards |
| topic | Dynamical Systems Geometric Topology 37A25, 37E35, 30F60, 32G15 |
| url | https://arxiv.org/abs/2003.00890 |