2 papers
math.DS2025
Complexity for billiards in regular N-gons
Jayadev Athreya, Pascal Hubert, Serge Troubetzkoy
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-Hube…
math.DS2023
On the complexity of polygonal billiards
Tyll Krueger, Arnaldo Nogueira, Serge Troubetzkoy
We show that the complexity of the billiard in a typical polygon grows cubically and the number of saddle connections grows quadratically along certain subsequences. It is known th…