Symmetric Relative Equilibria in the Four-Vortex Problem with Three Equal Vorticities

Ernesto Perez-Chavela; Manuele Santoprete; Claudia Tamayo

Symmetric Relative Equilibria in the Four-Vortex Problem with Three Equal Vorticities

Mathematical Physics 2017-10-10 v1 math.MP

Authors: Ernesto Perez-Chavela , Manuele Santoprete , Claudia Tamayo

Abstract

We examine in detail the relative equilibria of the 4-vortex problem when three vortices have equal strength, that is, $\Gamma_{1} = \Gamma_{2} = \Gamma_{3} = 1$ , and $\Gamma_{4}$ is a real parameter. We give the exact number of relative equilibria and bifurcation values. We also study the relative equilibria in the vortex rhombus problem.

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@article{arxiv.1407.7151,
  title  = {Symmetric Relative Equilibria in the Four-Vortex Problem with Three Equal Vorticities},
  author = {Ernesto Perez-Chavela and Manuele Santoprete and Claudia Tamayo},
  journal= {arXiv preprint arXiv:1407.7151},
  year   = {2017}
}

Comments

21 pages, 4 figures. arXiv admin note: text overlap with arXiv:1301.6194 by other authors

Symmetric Relative Equilibria in the Four-Vortex Problem with Three Equal Vorticities

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