Analysis reveals that billiards in regular polygons show chaotic behavior as n increases, indicating arithmetic control in dynamics.
In this paper we study billiards in regular n -sided polygons and monodromy over Teichmüller curves from an arithmetic perspective. Our main results show that the combinatorics of billiards in a periodic direction s is controlled by the projection of s to a finite projective line.This arithmetic control coexists, experimentally, with chaotic behavior that first emerges when n=12 .
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Curtis T. McMullen (2025) studied this question.
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