A geometric dynamical system with relation to billiards
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2021
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915040801587200 |
|---|---|
| author | Everett, Samuel |
| author_facet | Everett, Samuel |
| contents | We introduce a geometric dynamical system where iteration is defined as a cycling composition of different maps acting on a space composed of three or more lines in $\mathbb{R}^2$. This system is motivated by the dynamics of iterated function systems, as well as billiards with modified reflection laws. We provide conditions under which this dynamical system generates periodic orbits, and use this result to prove the existence of closed nonsmooth curves over $\mathbb{R}^2$ which satisfy particular structural constraints with respect to a space of intersecting lines in the plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_02207 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A geometric dynamical system with relation to billiards Everett, Samuel Dynamical Systems 37E99 (Primary) 51N20, 37C27 (Secondary) We introduce a geometric dynamical system where iteration is defined as a cycling composition of different maps acting on a space composed of three or more lines in $\mathbb{R}^2$. This system is motivated by the dynamics of iterated function systems, as well as billiards with modified reflection laws. We provide conditions under which this dynamical system generates periodic orbits, and use this result to prove the existence of closed nonsmooth curves over $\mathbb{R}^2$ which satisfy particular structural constraints with respect to a space of intersecting lines in the plane. |
| title | A geometric dynamical system with relation to billiards |
| topic | Dynamical Systems 37E99 (Primary) 51N20, 37C27 (Secondary) |
| url | https://arxiv.org/abs/2112.02207 |