English

On shadowing and hyperbolicity for geodesic flows on surfaces

Dynamical Systems 2017-06-29 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1605.03332,
  title  = {On shadowing and hyperbolicity for geodesic flows on surfaces},
  author = {Mario Bessa and Maria Joana Torres and Joao Lopes Dias},
  journal= {arXiv preprint arXiv:1605.03332},
  year   = {2017}
}

Comments

12 pages, 1 figure

R2 v1 2026-06-22T13:58:12.350Z