On the Hausdorff dimension of geodesics that diverge on average

2023/08/11 by Felipe Riquelme, Riquelme, Felipe, Aníbal Velozo +1
Mathematics · #28A78 #28D20 #37C45 #37D35 #37D40 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Morphological variations and asymmetry

paper · pdf · doi:10.48550/arxiv.2308.05894

openalex publication_date 2023/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we prove that the Hausdorff dimension of geodesic directions that are recurrent and diverge on average coincides with the entropy at infinity of the geodesic flow for any complete, pinched negatively curved Riemannian manifold. Furthermore, we prove that the entropy of a σ-finite, infinite, ergodic and conservative invariant measure is bounded from above by the entropy at infinity of the geodesic flow.

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