%0 Journal Article
%T Maximally and non-maximally fast escaping points of transcendental entire functions
%A D. J. Sixsmith
%J Mathematics
%D 2014
%I arXiv
%R 10.1017/S0305004115000018
%X We partition the fast escaping set of a transcendental entire function into two subsets, the maximally fast escaping set and the non-maximally fast escaping set. These sets are shown to have strong dynamical properties. We show that the intersection of the Julia set with the non-maximally fast escaping set is never empty. The proof uses a new covering result for annuli, which is of wider interest. It was shown by Rippon and Stallard that the fast escaping set has no bounded components. In contrast, by studying a function considered by Hardy, we give an example of a transcendental entire function for which the maximally and non-maximally fast escaping sets each have uncountably many singleton components.
%U http://arxiv.org/abs/1403.7362v1