Abstract:
The local case of A. Fomenko conjecture on the possibility of modeling Liouville foliations by integrable billiards is discussed. An extended version of its statements on numerical invariants on the edge of the Fomenko–Zieschang invariant of the Liouville foliation is proved. We show the realization of the Liouville foliation with some combinations of numerical marks values on a fixed edge by an appropriate class of integrable billiards.
\Bibitem{Ved21}
\by V.~V.~Vedyushkina
\paper Local modeling of Liouville foliations by billiards: implementation of edge invariants
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2021
\issue 2
\pages 28--32
\mathnet{http://mi.mathnet.ru/vmumm4388}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4300490}
\zmath{https://zbmath.org/?q=an:1478.37062}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2021
\vol 76
\issue 2
\pages 60--64
\crossref{https://doi.org/10.3103/S0027132221020091}
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This publication is cited in the following 10 articles:
D. A. Tuniyants, “Topology of isoenergetic surfaces of billiard books glued of rings”, Moscow University Mathematics Bulletin, 79:3 (2024), 130–141
V. A. Kibkalo, D. A. Tuniyants, “Uporyadochennye billiardnye igry i topologicheskie svoistva billiardnykh knizhek”, Trudy Voronezhskoi zimnei matematicheskoi shkoly S. G. Kreina — 2024, SMFN, 70, no. 4, Rossiiskii universitet druzhby narodov, M., 2024, 610–625
V. N. Zav'yalov, “Billiard with slipping by an arbitrary rational angle”, Sb. Math., 214:9 (2023), 1191–1211
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
Vladimir Dragović, Sean Gasiorek, Milena Radnović, “Billiard Ordered Games and Books”, Regul. Chaotic Dyn., 27:2 (2022), 132–150
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
Anatoly T. Fomenko, Vladislav A. Kibkalo, “Topology of Liouville foliations of integrable billiards on table-complexes”, European Journal of Mathematics, 8:4 (2022), 1392
A. T. Fomenko, V. V. Vedyushkina, “Billiards with Changing Geometry and Their Connection with the Implementation of the Zhukovsky and Kovalevskaya Cases”, Russ. J. Math. Phys., 28:3 (2021), 317
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