On the dynamical degree of surjective endomorphisms

Abstract

We establish a couple of dynamical properties of surjective rational maps $f:X⇢X$ for smooth projective surfaces $X$. We also give a numerical condition for regularity of $f$. Some explicit constructions and calculations, related to the topological entropy of $f$, are provided.

6 pages; v3: positivity condition in Definition 3.2 added