Generic Properties of Open Billiards

The purpose of this paper is to show that for a dense G set of three smooth d convex bodies with nowhere vanishing curvature in the Ck topology, 2FkF`., the open billiard obtained form these convex bodies determines a potential the one that defines the natural escape measure of this billiard. which is non-lattice. This result generalizes one of the results obtained in a previous work of A. Lopes and R. Markarian w1x.