Functions of genus zero for which the fast escaping set has Hausdorff dimension two
Complex Variables
2016-01-26 v1 Dynamical Systems
Abstract
We study a family of transcendental entire functions of genus zero, for which all of the zeros lie within a closed sector strictly smaller than a half-plane. In general these functions lie outside the Eremenko-Lyubich class. We show that for functions in this family the fast escaping set has Hausdorff dimension equal to two.
Keywords
Cite
@article{arxiv.1311.6987,
title = {Functions of genus zero for which the fast escaping set has Hausdorff dimension two},
author = {D. J. Sixsmith},
journal= {arXiv preprint arXiv:1311.6987},
year = {2016}
}