2021/10/14 by Paul Apisa, Apisa, Paul · 1 citation
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Mathematics and Applications #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2110.07540
openalex publication_date 2021/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.