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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
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.
Received: 21.09.2011 Accepted: 10.04.2012
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
Linking options:
https://www.mathnet.ru/eng/rcd415 https://www.mathnet.ru/eng/rcd/v17/i5/p451
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