99-222 Mirko Degli Esposti, Gianluigi Del Magno and Marco Lenci

Escape orbits and Ergodicity in Infinite Step Billiards (823K, Postscript) Jun 9, 99

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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.

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