Symmetric Liapunov center theorem for minimal orbit

Using the techniques of equivariant bifurcation theory we prove the existence of non-stationary periodic solutions of Γ-symmetric systems q¨(t)=−∇U(q(t)) in any neighborhood of an isolated orbit of minima Γ(q0) of the potential U. We show the strength of our result by proving the existence of new families of periodic orbits in the Lennard-Jones two- and three-body problems and in the Schwarzschild three-body problem.