Relative periodic solutions of the <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula>-vortex problem on the sphere

Abstract

This paper gives an analysis of the movement of \begin{document}$ n $\end{document} vortices on the sphere. When the vortices have equal circulation, there is a polygonal solution that rotates uniformly around its center. The main result concerns the global existence of relative periodic solutions that emerge from this polygonal relative equilibrium. In addition, it is proved that the families of relative periodic solutions contain dense sets of choreographies.