Description of peculiarities of the billiard system in domains bounded by confocal ellipses and hyperboles / V. V. Fokicheva. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2014. № 4. P. 6-17 [Moscow Univ. Math. Bulletin. Vol. 69, N 4, 2014.].
An integrable system that is a billiard in a domain bounded by confocal ellipses and hyperbolas is studied. This system arises in the description of the motion of a point inside this domain with natural reflection from the boundary. The topological invariant of Liouville equivalence of such systems, namely, the Fomenko-Zieschang molecule, is calculated using a new method developed by the author.
Key words: integrable system, billiards, Liouville equivalence, Fomenko-Zieschang molecule.