English

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}
}