The bifurcation analysis and the Conley index in mechanics


    2011, Vol. 7, No. 3, pp.  649-681

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

    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. New relative equilibria in the problem of the motion of point vortices of equal intensity in a circle are found.
    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, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 3, pp.  649-681
    DOI:10.20537/nd1103017


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