Transcendental Julia sets of positive finite Lebesgue measure

TL;DR

This paper demonstrates the existence of a transcendental entire function whose Julia set has positive finite Lebesgue measure, contributing to the understanding of the measure-theoretic properties of Julia sets.

Contribution

It constructs a specific transcendental entire function with a Julia set of positive finite Lebesgue measure, a novel result in complex dynamics.

Findings

Existence of transcendental entire functions with Julia sets of positive finite measure

Julia sets can have finite Lebesgue measure, contrary to previous assumptions

Provides a new example expanding the class of known Julia sets

Abstract

We show that there exists a transcendental entire function whose Julia set has positive finite Lebesgue measure.