Codimension one attracting sets in $\mathbb{P}^k(\mathbb{C})$

TL;DR

This paper investigates codimension one attracting sets in complex projective spaces, providing examples and analyzing their ergodic and pluripotential properties to deepen understanding of their dynamics.

Contribution

It introduces a large family of codimension one attracting sets of small topological degree and studies their ergodic and pluripotential theoretic characteristics.

Findings

Existence of a large family of such attracting sets.

Analysis of their ergodic properties.

Investigation of their pluripotential theoretic features.

Abstract

We are interested in attracting sets of $\mathbb{P}^k(\mathbb{C})$ which are of small topological degree and of codimension $1.$ We first show that there exists a large family of examples. Then we study their ergodic and pluripotential theoretic properties.