Liouville foliation of topological billiards in the Minkowski plane

In the paper, we give the Liouville classification of five interesting cases of topological billiards glued from two flat billiards bounded by arcs of confocal quadrics in the Minkowski plane. For each billiard, we calculate the marked Fomenko–Zieschang molecule, in other words the invariant of an integrable Hamiltonian system that completely determines the type of its Liouville foliation.