V. V. Vedyushkina, “The Liouville foliation of the billiard book modelling the Goryachev–Chaplygin case”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2020, no. 1, 64–68; Moscow University Mathematics, 75:1 (2020), 42

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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika

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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2020, Number 1, Pages 64–68 (Mi vmumm4305)

This article is cited in 15 scientific papers (total in 15 papers)

Short notes

The Liouville foliation of the billiard book modelling the Goryachev–Chaplygin case

V. V. Vedyushkina

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Full-text PDF (270 kB) Citations (15)

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Abstract: The Fomenko–Zieshang invariant of an interesting case of an integrable billiard book is calculated and it is shown that such a book models the dynamics of Goryachev–Chaplygin integrable case on a certain isoenergy surface.

Key words: integrable system, billiard, Liouville equivalence, Fomenko–Zieschang invariant.

Funding agency	Grant number
Russian Science Foundation	17-11-01303

Received: 19.12.2018

English version:
Moscow University Mathematics, 2020, Volume 75, Issue 1, Pages 42–46
DOI: https://doi.org/10.3103/S0027132220010076

Bibliographic databases:

Document Type: Article

UDC: 517.938.5

Language: Russian

Citation: V. V. Vedyushkina, “The Liouville foliation of the billiard book modelling the Goryachev–Chaplygin case”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2020, no. 1, 64–68; Moscow University Mathematics, 75:1 (2020), 42–46

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Linking options:

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https://www.mathnet.ru/eng/vmumm/y2020/i1/p64

This publication is cited in the following 15 articles:

D. A. Tuniyants, “Topology of isoenergetic surfaces of billiard books glued of rings”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2024, no. 3, 26–35
K. E. Turina, “Topological invariants of some ordered billiard games”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2024, no. 3, 19–25
K. E. Turina, “Topological invariants of some ordered billiard games”, Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 79:3 (2024), 122–129
D. A. Tuniyants, “Topology of isoenergetic surfaces of billiard books glued of rings”, Moscow University Mathematics Bulletin, Moscow University Mеchanics 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
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
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
V. A. Kibkalo, A. T. Fomenko, I. S. Kharcheva, “Realizing integrable Hamiltonian systems by means of billiard books”, Trans. Moscow Math. Soc., 82 (2021), 37–64
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
A. T. Fomenko, V. V. Vedyushkina, V. N. Zav'yalov, “Liouville Foliations of Topological Billiards with Slipping”, Russ. J. Math. Phys., 28:1 (2021), 37
Anatoly T. Fomenko, Vladislav A. Kibkalo, Understanding Complex Systems, Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics, 2021, 3

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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