Lyapunov Orbits in the $n$-Vortex Problem on the Sphere

In the phase space reduced by rotation, we prove the existence of periodic orbits of the $(n + 1)$-vortex problem emanating from a relative equilibrium formed by $n$ unit vortices at the vertices of a regular polygon at a fixed latitude and an additional vortex of intensity $\kappa$ at the north pole when the ideal fluid moves on the surface of a sphere.