Non-periodic not everywhere dense trajectories in triangular billiards
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911932524527616 |
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| author | Slipantschuk, Julia Bandtlow, Oscar F. Just, Wolfram |
| author_facet | Slipantschuk, Julia Bandtlow, Oscar F. Just, Wolfram |
| contents | Building on tools that have been successfully used in the study of rational billiards, such as induced maps and interval exchange transformations, we provide a construction of a one-parameter family of isosceles triangles exhibiting non-periodic trajectories that are not everywhere dense. This provides, by elementary means, a definitive negative answer to a long-standing open question on the density of non-periodic trajectories in triangular billiards. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17734 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-periodic not everywhere dense trajectories in triangular billiards Slipantschuk, Julia Bandtlow, Oscar F. Just, Wolfram Dynamical Systems 37C83, 37C79, 37B20, 37E30 Building on tools that have been successfully used in the study of rational billiards, such as induced maps and interval exchange transformations, we provide a construction of a one-parameter family of isosceles triangles exhibiting non-periodic trajectories that are not everywhere dense. This provides, by elementary means, a definitive negative answer to a long-standing open question on the density of non-periodic trajectories in triangular billiards. |
| title | Non-periodic not everywhere dense trajectories in triangular billiards |
| topic | Dynamical Systems 37C83, 37C79, 37B20, 37E30 |
| url | https://arxiv.org/abs/2406.17734 |