Another billiard problem
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917101371916288 |
|---|---|
| author | Bolotin, Sergey Treschev, Dmitry |
| author_facet | Bolotin, Sergey Treschev, Dmitry |
| contents | Let $(M,g)$ be a Riemannian manifold, $Ω\subset M$ a domain with boundary $Γ$, and $ϕ$ a smooth function such that $ϕ|_Ω> 0$, $\ph|_Γ= 0$, and $\nablaϕ|_Γ\ne 0$. We study the geodesic flow of the metric $G=g/ϕ$. The $G$-distance from any point of $Ω$ to $Γ$ is finite, hence the geodesic flow is incomplete. Regularization of the flow in a neighborhood of $Γ$ establishes a natural reflection law from $Γ$. This leads to a certain billiard problem in $Ω$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19203 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Another billiard problem Bolotin, Sergey Treschev, Dmitry Dynamical Systems Let $(M,g)$ be a Riemannian manifold, $Ω\subset M$ a domain with boundary $Γ$, and $ϕ$ a smooth function such that $ϕ|_Ω> 0$, $\ph|_Γ= 0$, and $\nablaϕ|_Γ\ne 0$. We study the geodesic flow of the metric $G=g/ϕ$. The $G$-distance from any point of $Ω$ to $Γ$ is finite, hence the geodesic flow is incomplete. Regularization of the flow in a neighborhood of $Γ$ establishes a natural reflection law from $Γ$. This leads to a certain billiard problem in $Ω$. |
| title | Another billiard problem |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2511.19203 |