English

The escaping set in transcendental dynamics

Dynamical Systems 2025-12-16 v1 Complex Variables

Abstract

The escaping set of an entire function consists of the points in the complex plane that tend to infinity under iteration. This set plays a central role in the dynamics of transcendental entire functions. The goal of this survey is to explain this role, to summarise some of the main results in the area, and to identify a number of open questions.

Keywords

Cite

@article{arxiv.2507.11370,
  title  = {The escaping set in transcendental dynamics},
  author = {Walter Bergweiler and Lasse Rempe},
  journal= {arXiv preprint arXiv:2507.11370},
  year   = {2025}
}

Comments

150 pages, 17 figures

R2 v1 2026-07-01T04:02:28.319Z