The bifurcation analysis and the Conley index in mechanics

A. V. Bolsinov ; A. V. Borisov ; I. S. Mamaev

Russian journal of nonlinear dynamics, Tome 7 (2011) no. 3, pp. 649-681.

Résumé

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.

Détail

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

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