Classifying relative equilibria. III

We announce several theorems on the evolution of relative equilibria classes in the planar n-body problem. In an earlier paper [1] we announced a partial classification of relative equilibria of four equal masses. In [2] we described these new relative equilibria classes and showed the way in which a degeneracy arose in the four body problem. These results point the way toward classifying relative equilibria for any n > 4.