Veech surfaces associated with rational billiards

Details Veech surfaces associated with rational billiards Veech surfaces associated with rational billiards

2002-05-23

arxiv.org/abs/math/0205249v1

Mathematics

Geometric Topology

5 pages

Scientific paper

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.

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