The Eremenko-Lyubich constant
Complex Variables
2024-12-10 v2 Dynamical Systems
Abstract
Eremenko and Lyubich proved that an entire function whose set of singular values is bounded is expanding at points where its image has large modulus. These expansion properties have been at the centre of the subsequent study of this class of functions, now called the Eremenko-Lyubich class. We improve the estimate of Eremenko and Lyubich, and show that the new estimate is asymptotically optimal. As a corollary, we obtain an elementary proof that functions in the Eremenko-Lyubich class have lower order at least .
Cite
@article{arxiv.2105.09053,
title = {The Eremenko-Lyubich constant},
author = {Lasse Rempe},
journal= {arXiv preprint arXiv:2105.09053},
year = {2024}
}
Comments
5 pages. V2: Author accepted manuscript; minor corrections from V1. To appear in Bull. London Math. Soc