On the stability conjecture for geodesic flows of manifold without conjugate points

Abstract : We study the C 2-structural stability conjecture from Mañé's viewpoint for geodesics flows of compact manifolds without conjugate points. The structural stability conjecture is an open problem in the category of geodesic flows because the C 1 closing lemma is not known in this context. Without the C 1 closing lemma, we combine the geometry of manifolds without conjugate points and a recent version of Franks' Lemma from Mañé's viewpoint to prove the conjecture for compact surfaces, for compact three dimensional manifolds with quasi-convex universal coverings where geodesic rays diverge, and for n-dimensional, generalized rank one manifolds.
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Contributor : Ludovic Rifford <>
Submitted on : Sunday, December 24, 2017 - 12:03:47 PM
Last modification on : Wednesday, December 12, 2018 - 1:18:34 AM

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Ludovic Rifford, Rafael Ruggiero. On the stability conjecture for geodesic flows of manifold without conjugate points. 2018. ⟨hal-01662529⟩

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