Escape orbits and Ergodicity in Infinite Step Billiards

Degli-Esposti, Mirko; Del Magno, Gianluigi; Lenci, Marco

Escape orbits and Ergodicity in Infinite Step Billiards

Authors

Degli-Esposti, Mirko

Del Magno, Gianluigi

Lenci, Marco

Description

In a previous paper we defined a class of non-compact polygonal billiards, the infinite step billiards: to a given decreasing sequence of non-negative numbers $\{p_{n}$, there corresponds a table $\Bi := \bigcup_{n\in\N} [n,n+1] \times [0,p_{n}]$. In this article, first we generalize the main result of the previous paper to a wider class of examples. That is, a.s. there is a unique escape orbit which belongs to the alpha and omega-limit of every other trajectory. Then, following a recent work of Troubetzkoy, we prove that generically these systems are ergodic for almost all initial velocities, and the entropy with respect to a wide class of ergodic measures is zero.
27 pages, 8 figures