On the measures of maximal entropy for the geodesic flow

Let M be a closed and connected manifold equipped with a C∞ Riemannian metric. Using the geodesic arc formalism developed by Ma ñ é (J. Differential Geom. 45 (1997) 74–93) and Paternain [Ann. Sci. École Norm. Sup. 4eme série t 33 (2000) 121–138], we give a way of constructing a measure of maximal entropy for the geodesic flow.