Journal of Statistical Physics, Vol. 83, Nos. 1/2, 1996, p. 39-70.
We discuss Liouville's theorem for nonsmooth integrable systems of the billiard
type and give a scheme of calculation of angle-action variables for the flow. We
also deal with the problem of pseudointegrability. We discuss the relationship
between the continuous-time (flow) and the discrete-time (map) approaches. We
treat all these aspects through a specific billiard — a wedge embedded in a two-
dimensional isotropic harmonic potential. Varying the parameters provides two
integrable and two pseudointegrable cases. It turns out that the dynamics of one
of the latter is indeed integrable in a certain sense. We also address the problem
of applying perturbation theory.