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Are Devaney hairs fast escaping?

Rempe, Lasse; Rippon, Philip J. and Stallard, Gwyneth M. (2010). Are Devaney hairs fast escaping? Journal of Difference Equations and Applications, 16(5&6) pp. 739–762.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1080/10236190903282824
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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.

Item Type: Journal Article
Copyright Holders: 2010 Taylor & Francis
ISSN: 1563-5120
Keywords: transcendental entire functions; iteration; Devaney hairs; fast escaping set
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 23231
Depositing User: Philip Rippon
Date Deposited: 23 Sep 2010 08:46
Last Modified: 05 Dec 2012 15:43
URI: http://oro.open.ac.uk/id/eprint/23231
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