On shadowing and hyperbolicity for geodesic flows on surfaces.

We prove that the geodesic flow on closed surfaces displays a hyperbolic set if the shadowing property holds C 2 -robustly on the metric. Similar results are obtained when considering even feeble properties like the weak shadowing and the specification properties. Despite the Hamiltonian nature of the geodesic flow, the arguments in the present paper differ completely from those used in Bessa et al. (2013) for Hamiltonian systems. [ABSTRACT FROM AUTHOR]