Generic properties of open billiards (Q1353832)

Open billiards were previously studied by the \textit{A. Lopes} and \textit{R. Markarian} in [SIAM J. Appl. Math. 56, No. 2, 651-680 (1996; Zbl 0852.58056)]. One of the results obtained there is that for a dense set of values \(a>2\), open billiards determined by three circles of radius one, centered in the vertices of an equilateral triangle of side \(a\), satisfy that the associated natural potential is a nonlattice. The aim of the present paper is to generalize such results by showing that for a dense \(G_{\delta}\) set of three convex bodies with nowhere vanishing curvature (in the \(C^k\) topology, \(2\leq k\leq \infty\)) the open billiard obtained from these convex bodies determines a potential (the one that defines the natural escape measure of this billiard) which is nonlattice.