2012/08/16 by Rippon, P. J., Stallard, G. M. · 1 citation
#30D05 #37F10 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1208.3371
We show that the fast escaping set A(f) of a transcendental entire function f has a structure known as a spider's web whenever the maximum modulus of f 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.