On noncompact bifurcation in one generalized model of vortex dynamics View Full Text


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Article Info

DATE

2022-07-26

AUTHORS

G. P. Palshin

ABSTRACT

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. More... »

PAGES

972-983

References to SciGraph publications

  • 1970-12. Topology and mechanics. I in INVENTIONES MATHEMATICAE
  • 2015-01. Bifurcation diagrams of natural Hamiltonian systems on Bertrand manifolds in MOSCOW UNIVERSITY MATHEMATICS BULLETIN
  • 2019-07. Bifurcation Diagram of One Generalized Integrable Model of Vortex Dynamics in REGULAR AND CHAOTIC DYNAMICS
  • 2021-11. Dynamics of a Circular Cylinder and Two Point Vortices in a Perfect Fluid in REGULAR AND CHAOTIC DYNAMICS
  • 2017-11-16. Topological classification of the Goryachev integrable systems in the rigid body dynamics: non-compact case in LOBACHEVSKII JOURNAL OF MATHEMATICS
  • 2020-06-29. Noncompact Bifurcations of Integrable Dynamic Systems in JOURNAL OF MATHEMATICAL SCIENCES
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    DOI

    http://dx.doi.org/10.1134/s0040577922070078

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