Billiard in a triangle and quadratic homogeneous foliations on

Abstract: This Note is partly an announcement. We describe the geodesic foliation of the translation surface associated to a triangular billiard in terms of real and holomorphic foliations defined by quadratic homogeneous vector fields on . Our technique allows, in particular, to state the existence of real foliations by curves on arising from homogeneous quadratic vector fields and having a dense set of periodic orbits. To cite this article: F. Valdez, C. R. Acad. Sci. Paris, Ser. I 346 (2008). [Copyright &y& Elsevier]