Topological entropy of a rational map over a complete metrized field
Abstract
We prove that the topological entropy of any dominant rational self-map of a projective variety defined over a complete non-Archimedean field is bounded from above by the maximum of its dynamical degrees, thereby extending a theorem of Gromov and Dinh-Sibony from the complex to the non-Archimedean setting. We proceed by proving that any regular self-map which admits a regular extension to a projective model defined over the valuation ring has necessarily zero entropy. To this end we introduce the e-reduction of a Berkovich analytic space, a notion of independent interest.
Fields of Study & Subjects
advanced mathematical theories
Mathematical Dynamics and Fractals
Advanced Topology and Set Theory
Publication details
- Journal / source
- Annales Scientifiques de l École Normale Supérieure
- Publisher
- Societe Mathematique de France
- Publication date
- 22 April 2026
- Language
- EN