Complexity for billiards in regular N-gons
Abstract
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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.