Complexity for billiards in regular N-gons
Dynamical Systems
2025-06-25 v2 Complex Variables
Geometric Topology
Abstract
We compute the complexity of the billiard language of the regular Euclidean -gons (and other families of rational lattice polygons), answering a question posed by Cassaigne-Hubert-Troubetzkoy. Our key technical result is a counting result for saddle connections on lattice surfaces, when we count by combinatorial length.
Keywords
Cite
@article{arxiv.2502.17627,
title = {Complexity for billiards in regular N-gons},
author = {Jayadev Athreya and Pascal Hubert and Serge Troubetzkoy},
journal= {arXiv preprint arXiv:2502.17627},
year = {2025}
}
Comments
42 pages, 12 figures, updated proof of Lemma 4.8 (added auxiliary lemma Lemma 4.9 and some new figures)