Periodic orbit theory analysis of a family of deformed hemispherical billiard systems

We present a periodic orbit theory analysis of a novel three-dimensional billiard system, namely a quasispherical cavity with infinite walls along the conical boundary defined by θ = Θ, where θ is the standard polar angle; for Θ = π/2 this reduces to the special case of a hemispherical infinite well, while for Θ = π it is a spherical well with points along the negative z axis excluded. We focus especially on the connections between subsets of the energy eigenvalue space and their contributions to qualitatively different classes of closed orbits.