2002/05/23 by Samuel Lelièvre, Lelièvre, Samuel
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #math.GT
paper · pdf · doi:10.48550/arxiv.math/0205249
5 pages
arxiv created 2002/05/23 · openalex publication_date 2002/05/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A nice trick for studying the billiard flow in a rational polygon is to unfold the polygon along the trajectories. This gives rise to a translation or half-translation surface tiled by the original polygon, or equivalently an Abelian or quadratic differential. Veech surfaces are a special class of translation surfaces with a large group of affine automorphisms, and interesting dynamical properties. The first examples of Veech surfaces came from rational billiards. We first present the mathematical objects and fix some vocabulary and notation. Then we review known results about Veech surfaces arising from rational billiards. The interested reader will find annex tables on the author's web page.