ИСТИНА

Let us call a simple billiard is a compact, connected subset of a Minkowski plane whose boundary consists of arcs of quadrics of the family of confocal quadrics on this plane and does not contain nonconvex angles. We obtain a 2-dimensional, connected, orientable manifold called topological billiard as a result of isometric gluing of several simple billiards. This construction was proposed by V. V. Fokicheva [3]. V. Dragovich and M. Radnovich investigated the billiard in ellipse on Minkowski plane [2]. The rule of reflection in simple billiard preserves the angle of incidence and the angle of reflection in terms of Minkowski and preserves the vector of Euclidean velocity. The reflection in topological billiard is defined in the same way for common boundary arcs. If the mass point on one of the sheets of the billiard hits the gluing edge, it reflects and continues motion along the second sheet. Ergo, topological billiard has two integrals - the caustic parameter and the vector of Euclidean velocity. It turns out that this motion is integrable. I use Fomenko-Zieschang method to describe topological types of Liouville foliations of several topological billiards on Minkowski plane. This method is detailed in [1].