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: https://doi.org/10.1080/10236190903282824

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.

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