# 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

#### One Citation

Existence of Birkhoff sections for Kupka-Smale Reeb flows of closed contact 3-manifolds

- Mathematics
- 2021

A Reeb vector field satisfies the Kupka-Smale condition when all its closed orbits are non-degenerate, and the stable and unstable manifolds of its hyperbolic closed orbits intersect transversely. We… Expand

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