On the lengths of closed geodesics on a two-sphere

Let be an isolated closed geodesic of length on a compact Riemannian manifold which is homologically visible in the dimension of its index, and for which the index of the iterates has the maximal possible growth rate. We show that has a sequence , , of prime closed geodesics of length where and . The hypotheses hold in particular when is a two-sphere and the ``shortest' Lusternik-Schnirelmann closed geodesic is isolated and ``nonrotating'.