Billiards in right triangles and orbit closures in genus zero strata
Dynamical Systems
2021-10-15 v1 Geometric Topology
Abstract
The orbit closure of the unfolding of every rational right and isosceles triangle is computed and the asymptotic number of periodic billiard trajectories in these triangles is deduced. This follows by classifying all orbit closures of rank at least two in hyperelliptic components of strata of Abelian and quadratic differentials. Additionally, given a fixed set of angles, the orbit closure of the unfolding of all unit area rational parallelograms, isosceles trapezoids, and right trapezoids outside of a discrete set is determined.
Keywords
Cite
@article{arxiv.2110.07540,
title = {Billiards in right triangles and orbit closures in genus zero strata},
author = {Paul Apisa},
journal= {arXiv preprint arXiv:2110.07540},
year = {2021}
}
Comments
92 pages. 12 figures. Comments welcome!