American Institute of Mathematical Sciences

March  2012, 32(3): 1055-1063. doi: 10.3934/dcds.2012.32.1055

Veech groups, irrational billiards and stable abelian differentials

 1 Centro de Ciencias Matemáticas, UNAM, Campus Morelia, C.P. 58089, Morelia, Michoacán, Mexico

Received  May 2010 Revised  July 2011 Published  October 2011

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 $\rm SO(2,\mathbf{R})$ and we calculate their rank.
Citation: Ferrán Valdez. Veech groups, irrational billiards and stable abelian differentials. Discrete & Continuous Dynamical Systems, 2012, 32 (3) : 1055-1063. doi: 10.3934/dcds.2012.32.1055
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