Fatou-Bieberbach domains as basins of attraction of automorphisms tangent to the identity

TL;DR

This paper constructs a specific automorphism of complex two-dimensional space that has a basin of attraction biholomorphic to the origin, illustrating complex dynamics near degenerate characteristic directions.

Contribution

It demonstrates the existence of a Fatou-Bieberbach domain as a basin of attraction for an automorphism tangent to the identity in C^2, with a degenerate characteristic direction.

Findings

Existence of automorphism with basin biholomorphic to the origin

Basin of attraction associated with a degenerate characteristic direction

Advances understanding of complex dynamics in several variables

Abstract

We prove that there exists an automorphism of C^2 tangent to the identity with a domain of attraction to the origin, biholomorphic to the origin, along a degenerate characteristic direction.