Commuting functions in class K and families of wandering Baker domains

TL;DR

This paper extends results on Julia sets of commuting functions with essential singularities in class K, proving they coincide under certain conditions, and constructs functions with wandering Baker domains.

Contribution

It generalizes Julia set equality for commuting functions in class K and constructs new functions exhibiting wandering Baker domains.

Findings

Julia sets of commuting functions in class K are equal under certain conditions

Constructed functions in class K have wandering Baker domains

Extended results from entire functions to functions with essential singularities

Abstract

Given commuting functions f,g, with at most a countable compact set of essential singularities, recent results for entire functions are extended to prove that Julia sets match, J(f)=J(g), in a particular case in the class K. With this result on hand, a general form of functions in this class, is constructed with wandering Baker domains.