Entire functions for which the escaping set is a spider's web

TL;DR

This paper constructs new classes of transcendental entire functions with their escaping and fast escaping sets forming spider's webs, and explores their stability and construction methods.

Contribution

It introduces novel classes of entire functions with spider's web structures in their escaping sets and demonstrates their stability and construction via composition, differentiation, and integration.

Findings

Several new classes of functions with spider's web escaping sets

Stability of these classes under function modifications

Construction of examples through composition, differentiation, and integration

Abstract

We construct several new classes of transcendental entire functions, f, such that both the escaping set, I(f), and the fast escaping set, A(f), have a structure known as a spider's web. We show that some of these classes have a degree of stability under changes in the function. We show that new examples of functions for which I(f) and A(f) are spiders' webs can be constructed by composition, by differentiation, and by integration of existing examples. We use a property of spiders' webs to give new results concerning functions with no unbounded Fatou components.