Bessa, Mário2023-05-262023-05-262018M. Bessa, A Note on Expansiveness and Hyperbolicity for Generic Geodesic Flows, Mathematical Physics, Analysis and Geometry, 21, 2, 2018http://hdl.handle.net/10400.2/13858In this short note we contribute to the generic dynamics of geodesic flows associated to metrics on compact Riemannian manifolds of dimension ≥ 2. We prove that there exists a C2-residual subset R of metrics on a given compact Riemannian manifold such that if g∈R, then its associated geodesic flow φ_g(t) is expansive if and only if the closure of the set of periodic orbits of φgt is a uniformly hyperbolic set. For surfaces, we obtain a stronger statement: there exists a C2-residual R such that if g ∈ R, then its associated geodesic flow φgt is expansive if and only if φ_g(t) is an Anosov flow.engExpansivenessResidual setsAnosovGeodesic flowsjournal article10.1007/s11040-018-9271-7