Work

Entropy stability and Milnor–Thurston invariants for Bowen–Series-like maps

Year: 2025

Type: article

Abstract: We define a family of discontinuous maps on the circle, called Bowen–Series-like maps, for geometric presentations of surface groups. The family has $2N$ parameters, where $2N$ is the number of generators of the presentation. We prove that all maps in the family have the same topological entropy, which coincides with the volume entropy of the group presentation. This approach allows a simple algorithmic computation of the volume entropy from the presentation only, using the Milnor–Thurston theory for one-dimensional maps.

Source: Ergodic Theory and Dynamical Systems

DOI: 10.1017/etds.2025.10245

Authors: LLUÍS ALSEDÀ, DAVID JUHER, JÉRÔME LOS, FRANCESC MAÑOSAS

Institutions: Universitat de Girona, Centre National de la Recherche Scientifique, Aix-Marseille Université

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Ministerio de Ciencia, Innovación y Universidades, Generalitat de Catalunya, Agència de Gestió d'Ajuts Universitaris i de Recerca