Stability of Relative Equilibria of Point Vortices on the Sphere

We describe the linear and nonlinear stability and instability of certain configurations of point vortices on the sphere forming relative equilibria. These configurations consist of up to two rings, with and without polar vortices. Such configurations have dihedral symmetry, and the symmetry is used both to block diagonalize the relevant matrices and to distinguish the subspaces on which their eigenvalues need to be calculated