The stability conjecture for geodesic flows of compact manifolds without conjugate points and quasi-convex universal covering

2023/11/21 by Rafaël Potrie, Potrie, Rafael, Rafael O. Ruggiero +1
Mathematics · #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2311.12979

openalex publication_date 2023/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (M,g) be a C^∞ compact, boudaryless connected manifold without conjugate points with quasi-convex universal covering and divergent geodesic rays. We show that the geodesic flow of (M,g) is C²-structurally stable from Mañé's viewpoint if and only if it is an Anosov flow, proving the so-called C¹-stability conjecture.

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