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.