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- W4386876241 abstract "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." @default.
- W4386876241 created "2023-09-20" @default.
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- W4386876241 date "2023-09-18" @default.
- W4386876241 modified "2023-09-27" @default.
- W4386876241 title "Chaotic properties for billiards in circular polygons" @default.
- W4386876241 doi "https://doi.org/10.48550/arxiv.2309.09892" @default.
- W4386876241 hasPublicationYear "2023" @default.
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