2022/07/08 by Jon Chaika, Samantha Fairchild, Chaika, Jon +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2207.03836
openalex publication_date 2022/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A translation surface is given by polygons in the plane, with sides identified by translations to create a closed Riemann surface with a flat structure away from finitely many singular points. Understanding geodesic flow on a surface involves understanding saddle connections. Saddle connections are the geodesics starting and ending at these singular points and are associated to a discrete subset of the plane. To measure the behavior of saddle connections of length at most R, we obtain precise decay rates as R→ ∞ for the difference in angle between two almost horizontal saddle connections.