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Sbornik: Mathematics, 2002, Volume 193, Issue 8, Pages 1103–1138
DOI: https://doi.org/10.1070/SM2002v193n08ABEH000672 (Mi sm672) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Topological analysis of the two-centre problem on the two-dimensional sphere

T. G. Vozmischeva, A. A. Oshemkov

M. V. Lomonosov Moscow State University
English version PDF (836 kB) Citations (13)
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DOI: https://doi.org/10.1070/SM2002v193n08ABEH000672
Abstract: The two-centre problem on the two-dimensional sphere (with the standard metric of constant positive curvature) is investigated from the topological point of view. The Fomenko–Zieschang invariants are constructed, which completely describe the topology of the Liouville foliations on isoenergy surfaces of this system. Various types of motion in the configuration space (regular motions and limit motions corresponding to bifurcations of Liouville tori) are described. The connection between Fomenko–Zieschang invariants (marked molecules) and various types of motion is considered.
Received: 23.10.2001
Russian version:
Matematicheskii Sbornik, 2002, Volume 193, Number 8, Pages 3–38
DOI: https://doi.org/10.4213/sm672
Bibliographic databases:
UDC: 515.1+521
MSC: 37J35, 70H06, 70F05
Language: English
Original paper language: Russian
Citation: T. G. Vozmischeva, A. A. Oshemkov, “Topological analysis of the two-centre problem on the two-dimensional sphere”, Sb. Math., 193:8 (2002), 1103–1138
Citation in format AMSBIB
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\by T.~G.~Vozmischeva, A.~A.~Oshemkov
\paper Topological analysis of the~two-centre problem on the~two-dimensional
sphere
\jour Sb. Math.
\yr 2002
\vol 193
\issue 8
\pages 1103--1138
\mathnet{http://mi.mathnet.ru//eng/sm672}
\crossref{https://doi.org/10.1070/SM2002v193n08ABEH000672}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1934542}
\zmath{https://zbmath.org/?q=an:1036.37021}
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\elib{https://elibrary.ru/item.asp?id=13408456}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0036662140}
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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:50
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