On shadowing and hyperbolicity for geodesic flows on surfaces

Bessa, Mário; Dias, João Lopes; Torres, Maria Joana

http://hdl.handle.net/10400.2/13863

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Authors

Bessa, Mário

Dias, João Lopes

Torres, Maria Joana

Abstract(s)

We prove that the geodesic flow on closed surfaces displays a hyperbolic set if the shadowing property holds C2-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.