Veech groups, irrational billiards and stable abelian differentials

2009/05/11 by Ferran Valdez, Valdez, Ferran
Mathematics · #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #math.DG #math.DS

paper · pdf · doi:10.48550/arxiv.0905.1591

8 pages, 2 figures

arxiv created 2009/06/29 · arxiv updated 2009/12/01

Abstract

We describe Veech groups of flat surfaces arising from irrational angled polygonal billiards or irreducible stable abelian differentials. For irrational polygonal billiards, we prove that these groups are non-discrete subgroups of SO(2,R) and we calculate their rank.

Related

• Veech surfaces associated with rational billiards
• Veech groups of flat structures on Riemann surfaces
• Looking for a Billiard Table which is not a Lattice Polygon but Satisfies Veech's Dichotomy
• Monodromy Groups of Dessins d'Enfant on Rational Polygonal Billiards Surfaces
• Notes on the Veech group of the Chamanara surface