Abstract:
A new class of integrable billiard systems, called generalized billiards, is discovered. These are billiards in domains formed by gluing classical billiard domains along pieces of their boundaries. (A classical billiard domain is a part of the plane bounded by arcs of confocal quadrics.) On the basis of the Fomenko-Zieschang theory of invariants of integrable systems, a full topological classification of generalized billiards is obtained, up to Liouville equivalence.
Bibliography: 18 titles.
Citation:
V. V. Fokicheva, “A topological classification of billiards in locally planar domains bounded by arcs of confocal quadrics”, Sb. Math., 206:10 (2015), 1463–1507
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\pages 1463--1507
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This publication is cited in the following 58 articles:
G. V. Belozerov, A. T. Fomenko, “Orbital invariants of billiards and linearly integrable geodesic flows”, Sb. Math., 215:5 (2024), 573–611
G. V. Belozerov, A. T. Fomenko, “Rotation Functions of Integrable Billiards As Orbital Invariants”, Dokl. Math., 2024
S. E. Pustovoitov, “Issledovanie struktury sloeniya Liuvillya integriruemogo ellipticheskogo billiarda s polinomialnym potentsialom”, Chebyshevskii sb., 25:1 (2024), 62–102
G. V. Belozerov, A. T. Fomenko, “Rotation functions of integrable billiards as orbital invariants”, Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, 515:1 (2024), 5
K. E. Turina, “Topological invariants of some ordered billiard games”, Moscow University Mathematics Bulletin, 79:3 (2024), 122–129
D. A. Tuniyants, “Topology of isoenergetic surfaces of billiard books glued of rings”, Moscow University Mathematics Bulletin, 79:3 (2024), 130–141
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V. A. Kibkalo, “Parabolicity of degenerate singularities in axisymmetric Euler systems with a gyrostat”, Moscow University Mathematics Bulletin, 78:1 (2023), 28–36
G. V. Belozerov, “Geodesic flow on an intersection of several confocal quadrics in $\mathbb{R}^n$”, Sb. Math., 214:7 (2023), 897–918
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M. A. Nikulin, “Spectrum of the Schrödinger operator in an elliptical ring cover”, Moscow University Mathematics Bulletin, 78:5 (2023), 230–243
S.E. Pustovoitov, “Classification of Singularities of the Liouville Foliation of an Integrable Elliptical Billiard with a Potential of Fourth Degree”, Russ. J. Math. Phys., 30:4 (2023), 643
G. V. Belozerov, “Topological classification of billiards bounded by confocal quadrics in three-dimensional Euclidean space”, Sb. Math., 213:2 (2022), 129–160
V. V. Vedyushkina, A. I. Skvortsov, “Topology of integrable billiard in an ellipse on the Minkowski plane with the Hooke potential”, Moscow University Mathematics Bulletin, 77:1 (2022), 7–19
Vladimir Dragović, Sean Gasiorek, Milena Radnović, “Billiard Ordered Games and Books”, Regul. Chaotic Dyn., 27:2 (2022), 132–150
A. T. Fomenko, V. V. Vedyushkina, “Evolutionary force billiards”, Izv. Math., 86:5 (2022), 943–979
V. V. Vedyushkina, V. N. Zav'yalov, “Realization of geodesic flows with a linear first integral by billiards with slipping”, Sb. Math., 213:12 (2022), 1645–1664
G. V. Belozerov, “Topology of $5$-surfaces of a 3D billiard inside a triaxial ellipsoid with Hooke's potential”, Moscow University Mathematics Bulletin, 77:6 (2022), 277–289
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