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Shadowing of geodesics, weak stability of the geodesic flow and global hyperbolic geometry

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  • We extend some previous results concerning the relationship between weak stability properties of the geodesic flow of manifolds without conjugate points and the global geometry of the manifold. We focus on the study of geodesic flows of compact manifolds without conjugate points satisfying either the shadowing property or topological stability, and we prove for three dimensional manifolds that under these assumptions the fundamental groups of certain quasi-convex manifolds have the Preissmann's property. This result generalizes a similar one obtained for manifolds with bounded asymptote.
    Mathematics Subject Classification: 37D40, 37J45, 34D30.


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