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Bifurcation analysis and the Conley index in mechanics. (English. Russian original) Zbl 1252.76055
Regul. Chaotic Dyn. 17, No. 5, 451-478 (2012); translation from Nelineĭn. Din. 7, No. 3, 649–681 (2011).
Summary: 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.

MSC:
37J20 Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems
34C23 Bifurcation theory for ordinary differential equations
76M23 Vortex methods applied to problems in fluid mechanics
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