2024/12/14 by Nicola Cavallucci, Cavallucci, Nicola
Mathematics · #Geometric and Algebraic Topology #Mathematics and Applications #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2412.10801
We extend the classical Otal-Peigné's Theorem to the class of proper, Gromov-hyperbolic spaces that are line-convex. Namely, we prove that when a group acts discretely and virtually freely by isometries on a metric space in this class then its critical exponent equals the topological entropy of the geodesic flow of the quotient metric space. We also show examples of proper, Gromov-hyperbolic spaces that are not line-convex and for which the statement fails.