Transcendental Semigroup that has Simply Connected Fatou Components

TL;DR

This paper demonstrates the existence of a transcendental semigroup with at least one simply connected Fatou component, expanding understanding of complex dynamics in transcendental functions.

Contribution

It proves the existence of a non-trivial transcendental semigroup with simply connected Fatou components, a novel result in complex dynamics.

Findings

Existence of transcendental semigroup with simply connected Fatou component

Identification of wandering, pre-periodic, or periodic Fatou components

Advancement in understanding Fatou set structures in transcendental dynamics

Abstract

We prove that there exists a non-trivial transcendental semigroup S such that the wandering (or pre-periodic or periodic) components of Fatou set F(S) has at least a simply connected domain D.