Starting the study of outer length billiards
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908553510387712 |
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| author | Baracco, Luca Bernardi, Olga Fierobe, Corentin |
| author_facet | Baracco, Luca Bernardi, Olga Fierobe, Corentin |
| contents | We focus on the outer length billiard dynamics, acting on the exterior of a strictly-convex planar domain. We first show that ellipses are totally integrable. We then provide an explicit representation of first order terms for the formal Taylor expansion of the corresponding Mather's $β$-function. Finally, we provide explicit Lazutkin coordinates up to order 4. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11915 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Starting the study of outer length billiards Baracco, Luca Bernardi, Olga Fierobe, Corentin Dynamical Systems We focus on the outer length billiard dynamics, acting on the exterior of a strictly-convex planar domain. We first show that ellipses are totally integrable. We then provide an explicit representation of first order terms for the formal Taylor expansion of the corresponding Mather's $β$-function. Finally, we provide explicit Lazutkin coordinates up to order 4. |
| title | Starting the study of outer length billiards |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2504.11915 |