Functions of genus zero for which the fast escaping set has Hausdorff dimension two

Sixsmith, D. J. (2015). Functions of genus zero for which the fast escaping set has Hausdorff dimension two. Proceedings of the American Mathematical Society, 143(6) pp. 2597–2612.

DOI: https://doi.org/10.1090/S0002-9939-2015-12487-2

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.

Viewing alternatives

Metrics

Item Actions

Export

You can export this page using these formats Digital Object Identifier - DOI