Topological analysis of a billiard bounded by confocal quadrics in a potential field

Consider a billiard in a plane domain bounded by confocal ellipses and hyperbolae. A Hooke potential acts on a point mass. This dynamical systems turns out to be completely Liouville integrable. A topological analysis of the Liouville foliation of isoenergy manifolds at all possible levels of the Hamiltonian is performed and the complete Fomenko- Zieschang invariants (marked molecules) of these manifolds are constructed. Bibliography: 15 titles.