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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2011, Volume 7, Number 3, Pages 649–681
(Mi nd283)
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This article is cited in 3 scientific papers (total in 3 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.
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
Linking options:
https://www.mathnet.ru/eng/nd283 https://www.mathnet.ru/eng/nd/v7/i3/p649
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