  If we consider the moduli space of flat connections of a non trivial
principal SO(3)-bundle over a surface, then we can define a map from the set of
perturbed closed geodesics, below a given energy level, into families of
perturbed Yang-Mills connections depending on a small parameter. In this paper
we show that this map is a bijection and maps perturbed geodesics into
perturbed Yang-Mills connections with the same Morse index.
