Dynamical Estimates on a Class of Quadratic Polynomial Automorphisms of $\mathbb C^3$

TL;DR

This paper investigates the dynamics of a specific class of quadratic automorphisms of complex three-dimensional space, providing estimates that enhance understanding of their complex behavior.

Contribution

It offers new dynamical estimates for the fifth class of quadratic automorphisms of ^3, expanding the understanding of their irregular maps.

Findings

Derived bounds on dynamical behavior of these automorphisms

Identified key properties of irregular maps in the fifth class

Enhanced classification insights for quadratic automorphisms

Abstract

Quadratic automorphisms of $\mathbb C^3$ are classified up to affine conjugacy into seven classes by Forn$\ae$ss and Wu. Five of them contain irregular maps with interesting dynamics. In this paper, we focus on the maps in the fifth class and make some dynamical estimates for these maps.