Geodesic
Topological classification of integrable geodesic billiards on quadrics in three-dimensional Euclidean space
Sbornik. Mathematics, Tome 211 (2020) no. 11, pp. 1503-1538

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We consider geodesic billiards on quadrics in $\mathbb{R}^3$. We consider the motion of a point mass inside a billiard table, that is, inside a domain lying on a quadric bounded by finitely many quadrics confocal with the given one and having angles at corner points of the boundary equal to ${\pi}/{2}$. According to the well-known Jacobi-Chasles theorem this problem turns out to be integrable. We introduce an equivalence relation on the set of billiard tables and prove a theorem on their classification. We present a complete classification of geodesic billiards on quadrics in $\mathbb{R}^3$ up to Liouville equivalence. Bibliography: 19 titles.
Keywords: integrable system, geodesic billiard
Mots-clés : Liouville equivalence, Fomenko-Zieschang invariant. 
@article{SM_2020_211_11_a0,
     author = {G. V. Belozerov},
     title = {Topological classification of integrable geodesic billiards on quadrics in three-dimensional {Euclidean} space},
     journal = {Sbornik. Mathematics},
     pages = {1503--1538},
     publisher = {mathdoc},
     volume = {211},
     number = {11},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2020_211_11_a0/}
}
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G. V. Belozerov. Topological classification of integrable geodesic billiards on quadrics in three-dimensional Euclidean space. Sbornik. Mathematics, Tome 211 (2020) no. 11, pp. 1503-1538. http://geodesic.mathdoc.fr/item/SM_2020_211_11_a0/