  The aim of this paper is to prove the existence of periodic solutions to
symmetric Newtonian systems in any neighborhood of an isolated orbit of
equilibria. Applying equivariant bifurcation techniques we obtain a
generalization of the classical Lyapunov center theorem to the case of
symmetric potentials with orbits of non-isolated critical points. Our tool is
an equivariant version of the Conley index. To compare the indices we compute
cohomological dimensions of some orbit spaces.
