Billiards in regular polygons
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 .
Authors
- Curtis T. McMullen (ORCID: https://orcid.org/0000-0001-8417-9500)
Institutions
- Harvard University Press (US)
Publication Details
- Journal
- L’Enseignement Mathématique
- Published
- 2025-09-24
- DOI
- https://doi.org/10.4171/lem/1099
- Primary Topic
- Mathematics and Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00