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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2014, Number 4, Pages 18–27 (Mi vmumm331)  
This article is cited in 31 scientific papers (total in 31 papers)

Mathematics

Description of singularities for billiard systems bounded by confocal ellipses or hyperbolas

V. V. Fokicheva

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (651 kB) Citations (31)
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Abstract: An integrable system that is a billiard in a domain bounded by confocal ellipses and hyperbolas is studied. This system arises in the description of the motion of a point inside this domain with natural reflection from the boundary. The topological invariant of Liouville equivalence of such systems, namely, the Fomenko–Zieschang molecule, is calculated using a new method developed by the author.
Key words: integrable system, billiards, Liouville equivalence, Fomenko–Zieschang molecule.
Funding agency Grant number
Russian Foundation for Basic Research 10-01-00748-a
Ministry of Education and Science of the Russian Federation НШ-1410.2012.1
14.740.11.0794
11.G34.31.0054
Received: 20.06.2012
English version:
Moscow University Mathematics Bulletin, 2014, Volume 69, Issue 4, Pages 148–158
DOI: https://doi.org/10.3103/S0027132214040020
Bibliographic databases:
Document Type: Article
UDC: 517.938.5
Language: Russian
Citation: V. V. Fokicheva, “Description of singularities for billiard systems bounded by confocal ellipses or hyperbolas”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2014, no. 4, 18–27; Moscow University Mathematics Bulletin, 69:4 (2014), 148–158
Citation in format AMSBIB
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\paper Description of singularities for billiard systems bounded by confocal ellipses or hyperbolas
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2014
\issue 4
\pages 18--27
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3372782}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2014
\vol 69
\issue 4
\pages 148--158
\crossref{https://doi.org/10.3103/S0027132214040020}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84926628561}
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    • This publication is cited in the following 31 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:55
     
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