On the dynamical degree of surjective endomorphisms

TL;DR

This paper investigates the dynamical properties of surjective rational maps on smooth projective surfaces, providing a numerical characterization for regular maps on del Pezzo surfaces and exploring their topological entropy.

Contribution

It introduces new dynamical properties for surjective rational maps and offers a numerical criterion for regularity on del Pezzo surfaces, including explicit calculations.

Findings

Established dynamical properties of surjective rational maps

Provided a numerical characterization of regular maps on del Pezzo surfaces

Presented explicit constructions related to topological entropy

Abstract

We establish a couple of dynamical properties of surjective rational maps $f: X \dashrightarrow X$ for smooth projective surfaces $X$. We also give a numerical characterization of regular $f$ in the case when $X$ is a del Pezzo surface. Some explicit constructions and calculations, related to the topological entropy of $f$, are provided.