Univalent Wandering Domains in the Eremenko-Lyubich Class

TL;DR

This paper constructs a specific entire function in the Eremenko-Lyubich class with a wandering domain where the function is univalent on all iterates, revealing new dynamics in complex analysis.

Contribution

It introduces a novel construction of an entire function with a univalent wandering domain in the Eremenko-Lyubich class using Bishop's folding theorem.

Findings

Existence of a univalent wandering domain in class B

Bounded components of the wandering orbit

Wandering domain surrounded by the postcritical set

Abstract

We use the folding theorem of Bishop to construct an entire function $f$ in class $B$ and a wandering domain $U$ of $f$ such that $f$ restricted to $f^n(U)$ is univalent, for all $n \geq 0$. The components of the wandering orbit are bounded and surrounded by the postcritical set.