Hyperbolicity through stable shadowing for generic geodesic flows

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

http://hdl.handle.net/10400.2/13865

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Authors

Bessa, Mário

Dias, João Lopes

Torres, Maria Joana

Abstract(s)

We prove that the closure of the closed orbits of a generic geodesic flow on a closed Riemannian n ≥ 2 dimensional manifold is a uniformly hyperbolic set if the shadowing property holds C2-robustly on the metric. We obtain analogous results using weak specification and the shadowing property allowing bounded time reparametrization.

Keywords

Geodesic flow Hyperbolic sets Shadowing Specification

URI

http://hdl.handle.net/10400.2/13865

Citation

M. Bessa, J. L. Dias, M. J. Torres, Hyperbolicity through stable shadowing for generic geodesic flows, Physica D: Nonlinear Phenomena, 406, 132423, 2020