A new family of entire functions with no wandering domains

TL;DR

This paper introduces a new family of transcendental entire functions that lack wandering domains, advancing understanding in complex dynamics and the structure of Julia sets.

Contribution

It identifies a novel family of entire functions without wandering domains, utilizing recent results on Fatou components and postsingular sets.

Findings

New family of entire functions with no wandering domains

Julia set of a subfamily is the whole plane

Advances in understanding complex dynamics

Abstract

The issue of whether an analytic function has wandering domains has long been of interest in complex dynamics. Sullivan proved in 1985 that rational maps do not have wandering domains. On the other hand, several transcendental entire functions have wandering domains. Using recent results on the relationship between Fatou components and the postsingular set, we find a new family of transcendental entire functions that does not have wandering domains. We also prove that the Julia set of a certain subfamily is the whole plane.