Are Devaney hairs fast escaping?

Details Are Devaney hairs fast escaping? Are Devaney hairs fast escaping?

2009-04-08

arxiv.org/abs/0904.1403v1

J. Difference Equ. Appl., 16 (2010), no. 5-6, 739-762

Mathematics

Dynamical Systems

22 pages, 1 figure

Scientific paper

10.1080/10236190903282824

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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