Chaotic properties for billiards in circular polygons
| Autor: | Clarke, Andrew, Ramírez-Ros, Rafael |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study billiards in domains enclosed by circular polygons. These are closed $C^1$ strictly convex curves formed by finitely many circular arcs. We prove the existence of a set in phase space, corresponding to generic sliding trajectories close enough to the boundary of the domain, in which the return billiard dynamics is semiconjugate to a transitive subshift on infinitely many symbols that contains the full $N$-shift as a topological factor for any $N \in \mathbb{N}$, so it has infinite topological entropy. We prove the existence of uncountably many asymptotic generic sliding trajectories approaching the boundary with optimal uniform linear speed, give an explicit exponentially big (in $q$) lower bound on the number of $q$-periodic trajectories as $q \to \infty$, and present an unusual property of the length spectrum. Our proofs are entirely analytical. Comment: 42 pages, 7 figures |
| Databáze: | arXiv |
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