Mirko Degli Esposti, Gianluigi Del Magno and Marco Lenci
An Infinite Step Billiard 
(389K, Uuencoded and gzipped Postscript)

ABSTRACT.  A class of non-compact billiards is introduced, namely the infinite step
billiards, i.e., systems of a point particle moving freely in the domain
$\Omega = \bigcup_{n\in\N} [n,n+1] \times [0,p_n]$, with elastic 
reflections on the boundary; here $p_0 = 1, p_n > 0$ and $p_n$ vanishes 
monotonically. 
After describing some generic ergodic features of these dynamical
systems, we turn to a more detailed study of the example $p_n = 2^{-n}$. 
What plays an important role in this case are the so called escape 
orbits, that is, orbits going to $+\infty$ monotonically in the 
X-velocity. A fairly complete description of them is given. This
enables us to prove some results concerning the topology of the
dynamics on the billiard.