<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We study the relative equilibria in the 4-vortex problem when two of vorticities are equal to 1, and the other two equal to <italic>m</italic> are enough small. We prove that for <italic>m</italic> > 0 there is a unique concave kite relative equilibria. We also prove that there is a unique convex planar relative equilibria having two pairs of equal vorticities located at the adjacent vertices of the configuration and it is an isosceles trapezoid.</p></abstract>

We study the relative equilibria in the 4-vortex problem when two of vorticities are equal to 1, and the other two equal to m are enough small. We prove that for m > 0 there is a unique concave kite relative equilibria. We also prove that there is a unique convex planar relative equilibria having two pairs of equal vorticities located at the adjacent vertices of the configuration and it is an isosceles trapezoid.

Relative Equilibria in the 4-Vortex Problem Bifurcating from an Equilateral Triangle Configuration

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

We study the relative equilibria in the 4-vortex problem when two of vorticities are equal to 1, and the other two equal to m are enough small. We prove that...

Relative Equilibria in the 4-Vortex Problem Bifurcating from an Equilateral Triangle Configuration

Published Online: Jun 02, 2016

Page range: 301 - 310

Received: Feb 04, 2016

Accepted: Jun 02, 2016

DOI: https://doi.org/10.21042/AMNS.2016.1.00025

Keywords
n-vortex problem, relative equilibria, bifurcations of relative equilibria

© 2016 Ernesto Pérez-Chavela, Claudia Tamayo, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Fig. 2

Relative Equilibria in the 4-Vortex Problem Bifurcating from an Equilateral Triangle Configuration

Published Online: Jun 02, 2016

Page range: 301 - 310

Received: Feb 04, 2016

Accepted: Jun 02, 2016

DOI: https://doi.org/10.21042/AMNS.2016.1.00025

Keywordsn-vortex problem, relative equilibria, bifurcations of relative equilibria

© 2016 Ernesto Pérez-Chavela, Claudia Tamayo, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Fig. 2

Keywords
n-vortex problem, relative equilibria, bifurcations of relative equilibria