Green currents for quasi-algebraically stable meromorphic self-maps of CP^k

TL;DR

This paper constructs a canonical Green current for certain meromorphic self-maps of complex projective space, linking dynamical degrees to Julia sets and establishing foundational properties of these currents.

Contribution

It introduces a canonical Green current for quasi-algebraically stable maps with specific dynamical degree properties, advancing the understanding of complex dynamics in higher dimensions.

Findings

Constructed a Green current T_f for the maps

Proved the support of T_f is within the Julia set

Established a functional equation for T_f

Abstract

We construct a canonical Green current T_f for every quasi-algebraically stable meromorphic self-map f of CP^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 of f, which is thus non empty.