Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2011, Number 2, Pages 10–20 (Mi vmumm667)  
This article is cited in 5 scientific papers (total in 5 papers)

Mathematics

Saddle singularities of complexity $1$ of integrable Hamiltonian systems

A. A. Oshemkov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (451 kB) Citations (5)
Abstract: Properties of saddle singularities of rank $0$ and complexity $1$ for integrable Hamiltonian systems are studied. An invariant ($f_n$-graph) solving the problem of semi-local classification of saddle singularities of rank $0$ for an arbitrary complexity was constructed earlier by the author. In this paper, a more simple form of the invariant for singularities of complexity $1$ is obtained and some properties of such singularities are described in algebraic terms. In addition, the paper contains a list of saddle singularities of complexity $1$ for systems with three degrees of freedom.
Key words: integrable Hamiltonian systems, momentum mapping, non-degenerate singularities, topological invariants.
Funding agency Grant number
Russian Foundation for Basic Research 10-01-00748
Ministry of Education and Science of the Russian Federation НШ-3224.2010.1
2.1.1.3704
ГК 02.740.11.5213
Received: 23.12.2009
English version:
Moscow University Mathematics Bulletin, 2011, Volume 66, Issue 2, Pages 60–69
DOI: https://doi.org/10.3103/S0027132211020021
Bibliographic databases:
Document Type: Article
UDC: 517.938.5+515.164.15
Language: Russian
Citation: A. A. Oshemkov, “Saddle singularities of complexity $1$ of integrable Hamiltonian systems”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2011, no. 2, 10–20; Moscow University Mathematics Bulletin, 66:2 (2011), 60–69
Citation in format AMSBIB
\Bibitem{Osh11}
\by A.~A.~Oshemkov
\paper Saddle singularities of complexity $1$ of integrable Hamiltonian systems
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2011
\issue 2
\pages 10--20
\mathnet{http://mi.mathnet.ru/vmumm667}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2882188}
\zmath{https://zbmath.org/?q=an:1304.37039}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2011
\vol 66
\issue 2
\pages 60--69
\crossref{https://doi.org/10.3103/S0027132211020021}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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