2021/11/27 by Mei Rose Connor, Diana Davis, Connor, Mei Rose +11
Mathematics · #37E35 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2111.13971
openalex publication_date 2021/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The study of polygonal billiards, particularly those in the regular pentagon, has been the subject of two recent papers. One of these papers approaches the problem of discovering the periodic trajectories on the pentagon by identifying slopes of periodic directions with points in the Poincaré disk generated by hyperbolic isometric transformations. The other approach, coming from the other paper, transforms the double pentagon into a rectilinear translation surface called the 'golden L', where periodic directions are generated by a set of matrices associated with this surface in a special way. We connect and unify these two approaches, and use our unification of these results to generalize them to arbitrary 2g+1-sided regular polygons.