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Nelin. Dinam., 2011, Volume 7, Number 3, Pages 649–681 (Mi nd283)  

This article is cited in 2 scientific papers (total in 2 papers)

The bifurcation analysis and the Conley index in mechanics

A. V. Bolsinovab, A. V. Borisovcd, I. S. Mamaevdc

a School of Mathematics, Loughborough University, United Kingdom, LE11 3TU, Loughborough, Leicestershire
b M. V. Lomonosov Moscow State University, Leninskie Gory, Moscow, 119992, Russia
c Udmurt State University, Universitetskaya 1, Izhevsk, 426034 Russia
d Institute of Computer Science, Universitetskaya 1, Izhevsk, 426034 Russia

Abstract: The paper is concerned with the use of bifurcation analysis and the Conley index in Hamiltonian dynamical systems. We give the proof of the theorem on the appearance (disappearance) of fixed points in the case of the Morse index change. We find new relative equilibria in the problem of the motion of point vortices of equal intensity in a circle.

Keywords: Morse index; Conley index; bifurcation analysis; bifurcation diagram; Hamiltonian dynamics; fixed point; relative equilibrium

Full text: PDF file (865 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 532.527, 517.925+517.938.5
MSC: 76M23, 34A05
Received: 28.07.2011
Revised: 21.09.2011

Citation: A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “The bifurcation analysis and the Conley index in mechanics”, Nelin. Dinam., 7:3 (2011), 649–681

Citation in format AMSBIB
\Bibitem{BolBorMam11}
\by A.~V.~Bolsinov, A.~V.~Borisov, I.~S.~Mamaev
\paper The bifurcation analysis and the Conley index in mechanics
\jour Nelin. Dinam.
\yr 2011
\vol 7
\issue 3
\pages 649--681
\mathnet{http://mi.mathnet.ru/nd283}


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    This publication is cited in the following articles:
    1. S. V. Sokolov, S. M. Ramodanov, “Dvizhenie krugovogo tsilindricheskogo tverdogo tela, vzaimodeistvuyuschego s tochechnym vikhrem, v pole sily tyazhesti”, Nelineinaya dinam., 8:3 (2012), 617–628  mathnet
    2. S. V. Sokolov, “Dvizhenie krugovogo tsilindricheskogo tverdogo tela, vzaimodeistvuyuschego s $N$ tochechnymi vikhryami, v pole sily tyazhesti”, Nelineinaya dinam., 10:1 (2014), 59–72  mathnet
  • Нелинейная динамика
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