Computational Study of the Dynamics of an Asymmetric Wedge Billiard

Abstract

We introduce the asymmetric wedge billiard as a generalization of the wedge billiard first studied by Lehtihet and Miller in 1986. This is a billiard system in which the billiard ball moves under the influence of a constant gravitational field, colliding elastically with two wedge walls with the collisions obeying the reflection law. Collision maps are given from which derivatives and area-preservation (or lack thereof) were determined. Expressions for the fixed points of the collision maps were also calculated and discussed. Long-term dynamics were determined computationally from which we observed integrable, quasi-periodic and chaotic behavior which were all dependent on the wedge angles.