Green functions and weights of polynomial skew products on C^2

TL;DR

This paper investigates the dynamics of polynomial skew products on complex two-dimensional space, establishing the existence and properties of Green functions through weighted techniques, and connecting these to rational extensions in weighted projective spaces.

Contribution

It introduces weighted methods to prove the existence and regularity of Green functions for polynomial skew products, linking complex dynamics to weighted projective space extensions.

Findings

Existence of multiple Green functions for polynomial skew products

Green functions are continuous and plurisubharmonic

Connection established between dynamics and weighted projective space extensions

Abstract

We study the dynamics of polynomial skew products on C^2. By using suitable weights, we prove the existence of several types of Green functions. Largely, continuity and plurisubharmonicity follow. Moreover, it relates to the dynamics of the rational extensions to weighted projective spaces.