Abstract:
A detailed description of topology of integrable billiard systems is given. For elliptical billiards and geodesic billiards on ellipsoid, the corresponding Fomenko graphs are constructed.
\Bibitem{DraRad09}
\by V. Dragovi\'c, M. Radnovi\'c
\paper Bifurcations of Liouville tori in elliptical billiards
\jour Regul. Chaotic Dyn.
\yr 2009
\vol 14
\issue 4-5
\pages 479--494
\mathnet{http://mi.mathnet.ru/rcd977}
\crossref{https://doi.org/10.1134/S1560354709040054}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2551871}
\zmath{https://zbmath.org/?q=an:1229.37065}
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This publication is cited in the following 41 articles:
G. V. Belozerov, A. T. Fomenko, “Orbital invariants of billiards and linearly integrable geodesic flows”, Sb. Math., 215:5 (2024), 573–611
D. A. Tuniyants, “Topology of isoenergetic surfaces of billiard books glued of rings”, Moscow University Mathematics Bulletin, 79:3 (2024), 130–141
Sean Gasiorek, Milena Radnović, Contemporary Mathematics, 807, Recent Progress in Special Functions, 2024, 111
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Vladimir Dragović, Sean Gasiorek, Milena Radnović, “Billiard Ordered Games and Books”, Regul. Chaotic Dyn., 27:2 (2022), 132–150
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Anatoly T. Fomenko, Vladislav A. Kibkalo, “Topology of Liouville foliations of integrable billiards on table-complexes”, European Journal of Mathematics, 8:4 (2022), 1392
Fomenko A.T., Vedyushkina V.V., “Billiards With Changing Geometry and Their Connection With the Implementation of the Zhukovsky and Kovalevskaya Cases”, Russ. J. Math. Phys., 28:3 (2021), 317–332
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E. E. Karginova, “Billiards bounded by arcs of confocal quadrics on the Minkowski plane”, Sb. Math., 211:1 (2020), 1–28
V. V. Vedyushkina, “Integrable billiard systems realize toric foliations on lens spaces and the 3-torus”, Sb. Math., 211:2 (2020), 201–225
G. V. Belozerov, “Topological classification of integrable geodesic billiards on quadrics in three-dimensional Euclidean space”, Sb. Math., 211:11 (2020), 1503–1538
Moskvin V.A., “Algorithmic Construction of Two-Dimensional Singular Fibers of Atoms of Billiards in Non-Convex Domains”, Mosc. Univ. Math. Bull., 75:3 (2020), 91–101
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