A sharp growth condition for a fast escaping spider's web
arXiv:1208.3371
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.