The second closed geodesic, the fundamental group, and generic Finsler metrics

For compact manifolds with infinite fundamental group we present sufficient topological or metric conditions ensuring the existence of two geometrically distinct closed geodesics. We also extend results about generic Riemannian metrics to Finsler metrics. We show a bumpy metrics theorem for Finsler metrics and prove that a C^4 -generic Finsler metric on a compact and simply-connected manifold carries infinitely many closed geodesics.