Bifurcations of critical orbits of invariant potentials with applications to bifurcations of central configurations of the N-body problem

In this article we study topological bifurcations of critical orbits of equivariant gradient equations. We give necessary and sufficient conditions for the existence of global bifurcations of solutions of these equations. Moreover, we apply these abstract results to the study of bifurcations of new families of planar central configurations of the N-body problem.