2025/02/24 by Athreya, Jayadev, Hubert, Pascal, Troubetzkoy, Serge
#30F30 #32G15 #37C83 #37E15 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2502.17627
We compute the complexity of the billiard language of the regular Euclidean N-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.