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Mathematics of the USSR-Sbornik, 1989, Volume 63, Issue 2, Pages 319–336
DOI: https://doi.org/10.1070/SM1989v063n02ABEH003276 (Mi sm1704) 		 
This article is cited in 18 scientific papers (total in 18 papers)

Round Morse functions and isoenergy surfaces of integrable Hamiltonian systems

S. V. Matveev, A. T. Fomenko, V. V. Sharko
English version PDF (1299 kB) Citations (18)
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DOI: https://doi.org/10.1070/SM1989v063n02ABEH003276
Abstract: A study is made of the topology of a class of three-dimensional manifolds that arise as constant energy surfaces for integrable systems. It is proved that this class coincides with the class of manifolds admitting a function all of whose critical manifolds are nondegenerate circles and whose nonsingular level surfaces are disjoint unions of tori. Necessary and sufficient conditions are obtained for the existence of minimal round Morse functions on manifolds of dimension greater than five.
Figures: 3.
Bibliography: 20 titles.
Received: 10.07.1986
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1988, Volume 135(177), Number 3, Pages 325–345
Bibliographic databases:
Document Type: Article
UDC: 513.944
MSC: Primary 58F05, 58F07, 57R65; Secondary 70H10
Language: English
Original paper language: Russian
Citation: S. V. Matveev, A. T. Fomenko, V. V. Sharko, “Round Morse functions and isoenergy surfaces of integrable Hamiltonian systems”, Mat. Sb. (N.S.), 135(177):3 (1988), 325–345; Math. USSR-Sb., 63:2 (1989), 319–336
Citation in format AMSBIB
\Bibitem{MatFomSha88}
\by S.~V.~Matveev, A.~T.~Fomenko, V.~V.~Sharko
\paper Round Morse functions and isoenergy surfaces of integrable Hamiltonian systems
\jour Mat. Sb. (N.S.)
\yr 1988
\vol 135(177)
\issue 3
\pages 325--345
\mathnet{http://mi.mathnet.ru/sm1704}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=937644}
\zmath{https://zbmath.org/?q=an:0673.58023}
\transl
\jour Math. USSR-Sb.
\yr 1989
\vol 63
\issue 2
\pages 319--336
\crossref{https://doi.org/10.1070/SM1989v063n02ABEH003276}
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  • https://www.mathnet.ru/eng/sm/v177/i3/p325
    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:669
    Russian version PDF:189
    English version PDF:23
    References:76
    First page:3
     
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