Geodesic
Topology of isoenergetic surfaces of billiard books glued of rings
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2024), pp. 26-35

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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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     author = {D. A. Tuniyants},
     title = {Topology of isoenergetic surfaces of billiard books glued of rings},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {26--35},
     publisher = {mathdoc},
     number = {3},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2024_3_a3/}
}
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D. A. Tuniyants. Topology of isoenergetic surfaces of billiard books glued of rings. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2024), pp. 26-35. http://geodesic.mathdoc.fr/item/VMUMM_2024_3_a3/