Continuation of relative equilibria in the $n$--body problem to spaces of constant curvature

Abimael Bengochea, Carlos García-Azpeitia, Ernesto Pérez-Chavela +1

We prove that all non-degenerate relative equilibria of the planar Newtonian $n$--body problem can be continued to spaces of constant curvature $\kappa$, positive or negative, for small…