2019/09/16 by Adam Abrams, Svetlana Katok, Abrams, Adam +3
Mathematics · #20H10 (Secondary) #28D20 #37D40 #37E10 (Primary) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1909.07032
openalex publication_date 2019/09/16 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
Given a closed, oriented, compact surface S of constant negative curvature\nand genus g \≥ 2, we study the measure-theoretic entropy of the Bowen-Series\nboundary map with respect to its smooth invariant measure. We obtain an\nexplicit formula for the entropy that only depends on the perimeter of the\n(8g-4)-sided fundamental polygon of the surface S and its genus. Using\nthis, we analyze how the entropy changes in the Teichm "uller space of S and\nprove the following flexibility result: the measure-theoretic entropy takes all\nvalues between 0 and a maximum that is achieved on the surface that admits a\nregular (8g-4)-sided fundamental polygon. We also compare the\nmeasure-theoretic entropy to the topological entropy of these maps and show\nthat the smooth invariant measure is not the measure of maximal entropy.\n