Mario Bessa, Maria Joana Torres, Joao Lopes Dias
Published 2016-05-11Version 1
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 [5] for Hamiltonian systems.
Comments: 12 pages, 1 figure
Escape of mass and entropy for geodesic flows
Singularity of projections of 2-dimensional measures invariant under the geodesic flow
Non-integrability of geodesic flow on certain algebraic surfaces
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