Rigidity of topological entropy of boundary maps associated to Fuchsian groups

2021/01/25 by Abrams, Adam, Katok, Svetlana, Ugarcovici, Ilie
#37D40 #37E10 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2101.10271

Abstract

Given a closed, orientable surface of constant negative curvature and genus g ≥ 2, we study a family of generalized Bowen-Series boundary maps and prove the following rigidity result: in this family the topological entropy is constant and depends only on the genus of the surface. We give an explicit formula for this entropy and show that the value of the topological entropy also stays constant in the Teichmüller space of the surface. The proofs use conjugation to maps of constant slope.

Related

• Flexibility of measure-theoretic entropy of boundary maps associated to\n Fuchsian groups
• Entropy stability and Milnor-Thurston invariants for Bowen-Series-like maps
• Volume entropy for surface groups via Bowen-Series like maps
• Entropy of embedded surfaces in quasi-fuchsian manifolds
• Flexibility of entropies for surfaces of negative curvature