[en] A new class of integrable billiard systems, called generalized billiards, is discovered. These are billiards in domains formed by gluing classical billiard domains along pieces of their boundaries. (A classical billiard domain is a part of the plane bounded by arcs of confocal quadrics.) On the basis of the Fomenko-Zieschang theory of invariants of integrable systems, a full topological classification of generalized billiards is obtained, up to Liouville equivalence. Bibliography: 18 titles

[en] We consider the billiard dynamical system in a domain bounded by confocal parabolas. We describe such domains in which the billiard problem can be correctly stated. In each such domain we prove the integrability for the system, analyse the arising Liouville foliation, and calculate the invariant of Liouville equivalence--the so-called marked molecule. It turns out that billiard systems in certain parabolic domains have the same closures of solutions (integral trajectories) as the systems of Goryachev-Chaplygin-Sretenskii and Joukowski at suitable energy levels. We also describe the billiard motion in noncompact domains bounded by confocal parabolas, namely, we describe the topology of the Liouville foliation in terms of rough molecules. Bibliography: 16 titles