Julia and escaping set spiders' webs of positive area

TL;DR

This paper investigates the dynamics of certain transcendental entire functions, demonstrating that their Julia, escaping, and fast escaping sets form spiders' webs with positive area, even outside the classical class B.

Contribution

It proves that for many such functions, the Julia and escaping sets are spiders' webs of positive area, a novel result especially outside class B.

Findings

Julia, escaping, and fast escaping sets are spiders' webs of positive area

Most functions studied lie outside the Eremenko-Lyubich class B

First known result on the area of a spider's web

Abstract

We study the dynamics of a collection of families of transcendental entire functions which generalises the well-known exponential and cosine families. We show that for functions in many of these families the Julia set, the escaping set and the fast escaping set are all spiders' webs of positive area. This result is unusual in that most of these functions lie outside the Eremenko-Lyubich class B. This is also the first result on the area of a spider's web.