Are Devaney hairs fast escaping?
Dynamical Systems
2010-07-29 v1 Complex Variables
Abstract
Beginning with Devaney, several authors have studied transcendental entire functions for which every point in the escaping set can be connected to infinity by a curve in the escaping set. Such curves are often called Devaney hairs. We show that, in many cases, every point in such a curve, apart from possibly a finite endpoint of the curve, belongs to the fast escaping set. We also give an example of a Devaney hair which lies in a logarithmic tract of a transcendental entire function and contains no fast escaping points.
Cite
@article{arxiv.0904.1403,
title = {Are Devaney hairs fast escaping?},
author = {Lasse Rempe and Philip J. Rippon and Gwyneth M. Stallard},
journal= {arXiv preprint arXiv:0904.1403},
year = {2010}
}
Comments
22 pages, 1 figure