More ergodic billiards with an infinite cusp

Abstract

In a previous paper (nlin.CD/0107041) the following class of billiards was studied: For $f:[0,+\infty )⟶(0,+\infty )$ convex, sufficiently smooth, and vanishing at infinity, let the billiard table be defined by $Q$, the planar domain delimited by the positive $x$-semiaxis, the positive $y$-semiaxis, and the graph of $f$. For a large class of $f$ we proved that the billiard map was hyperbolic. Furthermore we gave an example of a family of $f$ that makes this map ergodic. Here we extend the latter result to a much wider class of functions.

13 pages, 4 figures