Geodesic
On noncompact bifurcation in one generalized model of vortex dynamics
Teoretičeskaâ i matematičeskaâ fizika, Tome 212 (2022) no. 1, pp. 95-108 Cet article a éte moissonné depuis la source Math-Net.Ru

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A generalized model of Hamiltonian mechanics is considered. It includes two special cases: a model of the dynamics of three magnetic vortices in ferromagnets and a model of the dynamics of three hydrodynamic vortices in a perfect fluid. A constraint is imposed on the system by fixing one of the vortices at the point of origin. The system of the constrained problem of three magnetic vortices is a completely Liouville-integrable Hamiltonian system with two degrees of freedom. For this system, we find an augmented bifurcation diagram, perform a reduction to a system with one degree of freedom, and investigate level curves of the reduced Hamiltonian in detail. The obtained results show the presence of noncompact bifurcations and a noncritical bifurcation line.
Keywords: vortex dynamics, magnetic vortices, completely integrable Hamiltonian system, augmented bifurcation diagram, noncompact surgery, noncritical bifurcation curve. 
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     title = {On noncompact bifurcation in one generalized model of vortex dynamics},
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G. P. Palshin. On noncompact bifurcation in one generalized model of vortex dynamics. Teoretičeskaâ i matematičeskaâ fizika, Tome 212 (2022) no. 1, pp. 95-108. http://geodesic.mathdoc.fr/item/TMF_2022_212_1_a6/

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