From pathological to paradigmatic: A retrospective on Eremenko and Lyubich's entire functions
Dynamical Systems
2025-11-03 v1 Complex Variables
Abstract
This article surveys the impact of Eremenko and Lyubich's paper ''Examples of entire functions with pathological dynamics'', published in 1987 in the Journal of the LMS. Through a clever extension and use of classical approximation theorems, the authors constructed examples exhibiting behaviours previously unseen in holomorphic dynamics. Their work laid foundational techniques and posed questions that have since guided a good part of the development of transcendental dynamics.
Cite
@article{arxiv.2510.27356,
title = {From pathological to paradigmatic: A retrospective on Eremenko and Lyubich's entire functions},
author = {Núria Fagella and Leticia Pardo-Simón},
journal= {arXiv preprint arXiv:2510.27356},
year = {2025}
}
Comments
Survey article. To appear in the JLMS Centenary Special Issue