Topology of isoenergetic surfaces of billiard books glued of rings

D. A. Tuniyants

Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2024), pp. 26-35

Résumé

For an arbitrary billiard book glued from domains homeomorphic to annuli, it is shown that the isoenergy surface of the billiard dynamical system on such a table is homeomorphic to the direct product of the circle $S^1$ and the sphere $S^2$ with $g$ handles. In the class of ordered billiard games introduced by V. Dragovic and M. Radnovic and modeled by them later by means of billiard books (algorithmically constructed from the billiard ordered game), a subclass of those games was found, the simulation of which is possible only by means of billiard book subclass studied in this paper.

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