Mirko Degli Esposti, Gianluigi Del Magno and Marco Lenci
Escape orbits and Ergodicity in Infinite Step Billiards
(823K, Postscript)

ABSTRACT.  In \cite{ddl} we defined a class of non-compact polygonal billiard s, the \emph{infinite step \bi s}: to a given sequence of 
non-negative numbers $\{ p_{n} \}_{n\in\N}$, such that $p_{n} 
\searrow 0$, there corresponds a \emph{table} $\Bi := 
\bigcup_{n\in\N} [n,n+1] \times [0,p_{n}]$. 
In this article, first we generalize the main result of 
\cite{ddl} to a wider class of examples. That is, a.s.~there 
is a unique \emph{escape orbit} which belongs to the $\alpha$- and 
$\omega$-limit of every other \tr y. Then, following the 
recent work of Troubetzkoy \cite{tr}, we prove that 
\emph{generically} these systems are \erg\ for almost all 
initial velocities, and the entropy with respect to a wide 
class of ergodic merasures is zero.