Abstract:
A “billiard within an ellipse” is an integrable system appearing in the description of a point motion inside an ellipse with natural reflections at the boundary. This system is considered in the paper, the topological invariant of Liouville equivalence of this system is calculated, which is a Fomenko–Tsishang molecule, by the new method developed by the author.
Citation:
V. V. Fokicheva, “Description of singularities for system “billiard in an ellipse””, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, no. 5, 31–34; Moscow University Mathematics Bulletin, 67:5-6 (2012), 217–220
\Bibitem{Fok12}
\by V.~V.~Fokicheva
\paper Description of singularities for system ``billiard in an ellipse''
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2012
\issue 5
\pages 31--34
\mathnet{http://mi.mathnet.ru/vmumm527}
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\transl
\jour Moscow University Mathematics Bulletin
\yr 2012
\vol 67
\issue 5-6
\pages 217--220
\crossref{https://doi.org/10.3103/S0027132212050063}
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Linking options:
https://www.mathnet.ru/eng/vmumm527
https://www.mathnet.ru/eng/vmumm/y2012/i5/p31
This publication is cited in the following 22 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, “Geodesic flow on an intersection of several confocal quadrics in Rn”, Sb. Math., 214:7 (2023), 897–918
A. T. Fomenko, V. V. Vedyushkina, “Billiards and integrable systems”, Russian Math. Surveys, 78:5 (2023), 881–954
A. A. Kuznetsova, “Modeling of degenerate peculiarities of integrable billiard systems by billiard books”, Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 78:5 (2023), 207–215
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, V. A. Kibkalo, “Billiardnye knizhki maloi slozhnosti i realizatsiya sloenii Liuvillya integriruemykh sistem”, Chebyshevskii sb., 23:1 (2022), 53–82
Anatoly T. Fomenko, Vladislav A. Kibkalo, “Topology of Liouville foliations of integrable billiards on table-complexes”, European Journal of Mathematics, 8:4 (2022), 1392
V. V. Vedyushkina, “Orbital invariants of flat billiards bounded by arcs of confocal quadrics and containing focuses”, Moscow University Mathematics Bulletin, 76:4 (2021), 177–180
M Pnueli, V Rom-Kedar, “On the structure of Hamiltonian impact systems”, Nonlinearity, 34:4 (2021), 2611
V. V. Vedyushkina, “Integrable billiard systems realize toric foliations on lens spaces and the 3-torus”, Sb. Math., 211:2 (2020), 201–225
I. S. Kharcheva, “Isoenergy manifolds of integrable billiard books”, Moscow University Mathematics Bulletin, 75:4 (2020), 149–160
G. V. Belozerov, “Topological classification of integrable geodesic billiards on quadrics in three-dimensional Euclidean space”, Sb. Math., 211:11 (2020), 1503–1538
V. V. Vedyushkina, “The Fomenko–Zieschang invariants of nonconvex topological billiards”, Sb. Math., 210:3 (2019), 310–363
V. V. Vedyushkina (Fokicheva), A. T. Fomenko, “Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards”, Izv. Math., 83:6 (2019), 1137–1173
A. T. Fomenko, V. V. Vedyushkina, “Billiards and integrability in geometry and physics. New scope and new potential”, Moscow University Mathematics Bulletin, 74:3 (2019), 98–107
A. T. Fomenko, V. V. Vedyushkina, “Implementation of Integrable Systems by Topological, Geodesic Billiards with Potential and Magnetic Field”, Russ. J. Math. Phys., 26:3 (2019), 320
V. V. Vedyushkina, I. S. Kharcheva, “Billiard books model all three-dimensional bifurcations of integrable Hamiltonian systems”, Sb. Math., 209:12 (2018), 1690–1727
V. V. Vedyushkina (Fokicheva), A. T. Fomenko, “Integrable topological billiards and equivalent dynamical systems”, Izv. Math., 81:4 (2017), 688–733
I. V. Sypchenko, D. S. Timonina, “Closed geodesics on piecewise smooth surfaces of revolution with constant curvature”, Sb. Math., 206:5 (2015), 738–769
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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