Corpus ID: 237592726

Proof of the $C^2$-stability conjecture for geodesic flows of closed surfaces

@inproceedings{Contreras2021ProofOT,
  title={Proof of the \$C^2\$-stability conjecture for geodesic flows of closed surfaces},
  author={Gonzalo Contreras and Marco Mazzucchelli},
  year={2021}
}
We prove that a C2-generic Riemannian metric on a closed surface has either an elliptic closed geodesic or an Anosov geodesic flow. As a consequence, we prove the C2-stability conjecture for Riemannian geodesic flows of closed surfaces: a C2-structurally stable Riemannian geodesic flow of a closed surface is Anosov. In order to prove these statements, we establish a general result that may be of independent interest and provides sufficient conditions for a Reeb flow of a closed 3-manifold to be… Expand
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