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. 18-27
[Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].

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.