Equidistribution results for geodesic flows

2013 Ergodic Theory and Dynamical Systems  
Using the works of MañéMa and Paternain Pat we study the distribution of geodesic arcs with respect to equilibrium states of the geodesic flow on a closed manifold, equipped with a C^∞ Riemannian metric. We prove large deviations lower and upper bounds and a contraction principle for the geodesic flow in the space of probability measures of the unit tangent bundle. We deduce a way of approximating equilibrium states for continuous potentials.
doi:10.1017/etds.2012.153 fatcat:imp7lveqe5bq7evrukbj6nqdia