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On the dynamical degree of surjective endomorphisms

Ilya Karzhemanov

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.

On the dynamical degree of surjective endomorphisms

Abstract

We establish a couple of dynamical properties of surjective rational maps for smooth projective surfaces . We also give a numerical characterization of regular in the case when is a del Pezzo surface. Some explicit constructions and calculations, related to the topological entropy of , are provided.
Paper Structure (1 section, 2 theorems, 2 equations)

This paper contains 1 section, 2 theorems, 2 equations.

Table of Contents

  1. Introduction

Key Result

Proposition 1.2

$\lambda(f) = \rho(f^*)$ and there is a (Perron) vector $v \in N^1(X)$, which is a nef class on $X$, satisfying $f^*(v) = \lambda(f)v$.

Theorems & Definitions (4)

  • Proposition 1.2
  • Remark 1.3
  • Theorem 1.5
  • Remark 1.6