A sharp growth condition for a fast escaping spider's web
Dynamical Systems
2012-08-17 v1 Complex Variables
Abstract
We show that the fast escaping set of a transcendental entire function has a structure known as a spider's web whenever the maximum modulus of grows below a certain rate. We give examples of entire functions for which the fast escaping set is not a spider's web which show that this growth rate is best possible. By our earlier results, these are the first examples for which the escaping set has a spider's web structure but the fast escaping set does not. These results give new insight into a conjecture of Baker and a conjecture of Eremenko.
Cite
@article{arxiv.1208.3371,
title = {A sharp growth condition for a fast escaping spider's web},
author = {P. J. Rippon and G. M. Stallard},
journal= {arXiv preprint arXiv:1208.3371},
year = {2012}
}