Infinite step billiards

In [DDL] and [DDL2] (in collaboration with G. Del Magno e M. Lenci) we defined a class of non-compact polygonal billiards, the infinite step billiards: to a given sequence of non-negative numbers {p(n)}nis an element ofN, such that p(n) SE arrow 0, there corresponds a table P WEN [n, n + 1] X [0, p(n)]. The aim of this contribution is to overwiew some of these results. In particular we will focus on the ergodic and topological properties of these non-compact dynamical systesm. We show that generically these systems are ergodic for almost all initial velocities, and the entropy with respect to a wide class of measures is zero.