Green currents for quasi-algebraically stable meromorphic self-maps of $\mathbb{P}^k$

Abstract

We construct a canonical Green current $T_f$ for every quasi-algebraically stable meromorphic self-map $f$ of $\mathbb{P}^k$ such that its first dynamical degree $\lambda_1(f)$ is a simple root of its characteristic polynomial and that $\lambda_1(f)>1.$ We establish a functional equation for $T_f$ and show that the support of $T_f$ is contained in the Julia set, which is thus non empty.