Entire functions for which the escaping set is a spider's web
Complex Variables
2016-01-26 v1 Dynamical Systems
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.
Cite
@article{arxiv.1012.1303,
title = {Entire functions for which the escaping set is a spider's web},
author = {D. J. Sixsmith},
journal= {arXiv preprint arXiv:1012.1303},
year = {2016}
}