Constructing entire functions with non-locally connected Julia set by quasiconformal surgery

TL;DR

This paper presents a novel method using quasiconformal surgery to construct entire functions whose Fatou components are quasi-circles while their Julia sets are non-locally connected.

Contribution

It introduces an alternative construction technique for entire functions with specific dynamic properties, expanding the toolkit for complex dynamics research.

Findings

All Fatou components are quasi-circles.

Julia set is non-locally connected.

Method provides new examples in complex dynamics.

Abstract

We give an alternative way to construct an entire function with quasiconformal surgery so that all its Fatou components are quasi-circles but the Julia set is non-locally connected.