Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2019, Number 3, Pages 15–25 (Mi vmumm624)  

This article is cited in 4 scientific papers (total in 4 papers)

Mathematics

Billiards and integrability in geometry and physics. New scope and new potential

A. T. Fomenko, V. V. Vedyushkina

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Description of bifurcations and symmetries of integrable systems is an important branch of geometry that has many applications. Important results have been obtained recently in the descriptions of bifurcations of integrable billiards and in modelling of Hamiltonian systems of mechanics and dynamics by billiards. The paper contains interesting problems, as well as a research program for the near future. In the closing of the paper, the results allowing one to describe hidden symmetries of Hamiltonian bifurcations are given as an example of a work close to billiards subject.

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

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-6399.2018.1
Russian Foundation for Basic Research 16-01-00378-а


Full text: PDF file (360 kB)
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English version:
Moscow University Mathematics Bulletin, 2019, 74:3, 98–107

Bibliographic databases:

UDC: 517.938.5
Received: 23.01.2019

Citation: A. T. Fomenko, V. V. Vedyushkina, “Billiards and integrability in geometry and physics. New scope and new potential”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2019, no. 3, 15–25; Moscow University Mathematics Bulletin, 74:3 (2019), 98–107

Citation in format AMSBIB
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\pages 98--107
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. F. Kobtsev, “An elliptic billiard in a potential force field: classification of motions, topological analysis”, Sb. Math., 211:7 (2020), 987–1013  mathnet  crossref  crossref  mathscinet  isi  elib
    2. V. V. Vedyushkina, V. A. Kibkalo, “Realizatsiya bilyardami chislovogo invarianta rassloeniya Zeiferta integriruemykh sistem”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2020, no. 4, 22–28  mathnet
    3. G. V. Belozerov, “Topological classification of integrable geodesic billiards on quadrics in three-dimensional Euclidean space”, Sb. Math., 211:11 (2020), 1503–1538  mathnet  crossref  crossref  mathscinet  isi  elib
    4. V. V. Vedyushkina, “Lokalnoe modelirovanie bilyardami sloenii Liuvillya: realizatsiya rebernykh invariantov”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2021, no. 2, 28–32  mathnet
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