The Bifurcation Analysis and the Conley Index in Mechanics

    2012, Volume 17, Number 5, pp.  457-478

    Author(s): Bolsinov A. V., Borisov A. V., Mamaev I. S.

    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
    Citation: Bolsinov A. V., Borisov A. V., Mamaev I. S., The Bifurcation Analysis and the Conley Index in Mechanics, Regular and Chaotic Dynamics, 2012, Volume 17, Number 5, pp. 457-478

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