Geodesic Anosov flows, hyperbolic closed geodesics and stable ergodicity
Differential Geometry
2022-02-11 v1
Abstract
In this paper we show that the geodesic flow of a Finsler metric is Anosov if and only if there exists a open neighborhood of Finsler metrics all of whose closed geodesics are hyperbolic. For surfaces this result holds also for Riemannian metrics. This follows from a recent result of Contreras and Mazzucchelli. Furthermore, geodesic flows of Riemannian or Finsler metrics on surfaces are stably ergodic if and only if they are Anosov.
Cite
@article{arxiv.2202.05084,
title = {Geodesic Anosov flows, hyperbolic closed geodesics and stable ergodicity},
author = {Gerhard Knieper and Benjamin H. Schulz},
journal= {arXiv preprint arXiv:2202.05084},
year = {2022}
}
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8 pages