Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2019, Number 3, Pages 15–25 (Mi vmumm624)  
This article is cited in 22 scientific papers (total in 22 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
Full-text PDF (360 kB) Citations (22)
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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
Received: 23.01.2019
English version:
Moscow University Mathematics Bulletin, 2019, Volume 74, Issue 3, Pages 98–107
DOI: https://doi.org/10.3103/S0027132219030021
Bibliographic databases:
Document Type: Article
UDC: 517.938.5
Language: Russian
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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    • This publication is cited in the following 22 articles:
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