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Regular and Chaotic Dynamics, 2012, Volume 17, Issue 5, Pages 451–478
DOI: https://doi.org/10.1134/S1560354712050073 (Mi rcd415) 		 
This article is cited in 18 scientific papers (total in 18 papers)

The Bifurcation Analysis and the Conley Index in Mechanics

Alexey V. Bolsinovab, Alexey V. Borisovb, Ivan S. Mamaevb

a School of Mathematics, Loughborough University, United Kingdom, LE11 3TU, Loughborough, Leicestershire
b Institute of Computer Science, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
Citations (18)
DOI: https://doi.org/10.1134/S1560354712050073
Abstract: The paper is devoted to the bifurcation analysis and the Conley index in Hamiltonian dynamical systems. We discuss the phenomenon of appearance (disappearance) of equilibrium points under the change of the Morse index of a critical point of a Hamiltonian. As an application of these techniques we find new relative equilibria in the problem of the motion of three point vortices of equal intensity in a circular domain.
Keywords: Morse index, Conley index, bifurcation analysis, bifurcation diagram, Hamiltonian dynamics, fixed point, relative equilibrium.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 11.G34.31.0039
14.740.11.0876
NSh-2519.2012.1
This research was supported by the Grant of the Government of the Russian Federation for state support of scientific research conducted under supervision of leading scientists in Russian educational institutions of higher professional education (contract no. 11.G34.31.0039) and the federal target programme “Scientific and Scientific-Pedagogical Personnel of Innovative Russia” (14.740.11.0876). The work was supported by the Grant of the President of the Russian Federation for the Leading Scientific Schools of the Russian Federation (NSh-2519.2012.1).
Received: 21.09.2011
Accepted: 10.04.2012
Bibliographic databases:
Document Type: Article
MSC: 76M23, 34A05
Language: English
Citation: Alexey V. Bolsinov, Alexey V. Borisov, Ivan S. Mamaev, “The Bifurcation Analysis and the Conley Index in Mechanics”, Regul. Chaotic Dyn., 17:5 (2012), 451–478
Citation in format AMSBIB
\Bibitem{BolBorMam12}
\by Alexey V. Bolsinov, Alexey V. Borisov, Ivan S. Mamaev
\paper The Bifurcation Analysis and the Conley Index in Mechanics
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 5
\pages 451--478
\mathnet{http://mi.mathnet.ru/rcd415}
\crossref{https://doi.org/10.1134/S1560354712050073}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2989517}
\zmath{https://zbmath.org/?q=an:1252.76055}
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    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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