Irrational Fatou components in non-Archimedean dynamics

TL;DR

This paper explores the geometry of Fatou components in non-Archimedean dynamics, providing the first example of an irrational disk as a Fatou component through explicit computation of a wandering domain.

Contribution

It introduces the first example of an irrational disk as a Fatou component in non-Archimedean dynamics by explicitly computing a wandering domain.

Findings

First example of an irrational disk as a Fatou component

Explicit computation of a wandering domain in non-Archimedean dynamics

Advances understanding of Fatou component geometries

Abstract

This paper studies the geometry of Fatou components in non-Archimedean dynamics. By explicitly computing a wandering domain constructed by Benedetto, it provides the first example of a Fatou component that is an irrational disk.