Topological bifurcation of relative equilibria for the Kirchhoff 8-vortex problem

In this article we prove necessary and sufficient conditions for the existence of local and global bifurcations of relative equilibria of the 8-vortex problem. Applying the equivariant bifurcation theory we prove that from the families of regular concentric squares forming relative equilibria, bifurcate relative equilibria whose shape is more complicated.