Escape orbits and Ergodicity in Infinite Step Billiards

Details Escape orbits and Ergodicity in Infinite Step Billiards Escape orbits and Ergodicity in Infinite Step Billiards

1999-06-09

arxiv.org/abs/chao-dyn/9906017v1

Nonlinearity 13 (2000), no. 4, 1275-1292

Mathematics

Dynamical Systems

27 pages, 8 figures

Scientific paper

10.1088/0951-7715/13/4/316

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.

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