Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2011, Number 4, Pages 59–61 (Mi vmumm707)  
This article is cited in 1 scientific paper (total in 1 paper)

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Smooth invariants of focus-focus singularities

A. M. Izosimov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (333 kB) Citations (1)
Abstract: We consider focus–focus singularities of integrable Hamiltonian systems with two degrees of freedom. It is known that if two singularities of this kind have the same number of singular points, then they are fiber-wise homeomorphic. However, it may happen that this homeomorphism cannot be made smooth. An invariant has been constructed, which makes it possible to classify focus–focus singularities up to a $\mathrm{C}^1$-diffeomorphism.
Key words: Hamiltonian systems, singularities, integrability.
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
РНП-2.1.1.3704
02.740.11.5213
14.740.11.0794
Received: 24.12.2010
Bibliographic databases:
Document Type: Article
UDC: 517.938.5
Language: Russian
Citation: A. M. Izosimov, “Smooth invariants of focus-focus singularities”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2011, no. 4, 59–61
Citation in format AMSBIB
\Bibitem{Izo11}
\by A.~M.~Izosimov
\paper Smooth invariants of focus-focus singularities
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2011
\issue 4
\pages 59--61
\mathnet{http://mi.mathnet.ru/vmumm707}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2919097}
\zmath{https://zbmath.org/?q=an:1304.37036}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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