The escaping set in transcendental dynamics

2025/07/15 by Walter Bergweiler, Bergweiler, Walter, Lasse Rempe +1 · 2 citations
Psychology · #30D05 #37F10 #Academic and Historical Perspectives in Psychology #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2507.11370

openalex publication_date 2025/07/15 · openalex created_date 2025/10/09 · openalex updated_date 2026/07/29

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.

Cited by

• Simply Connected Wandering Domains of Small Order Entire Functions
• From pathological to paradigmatic: A retrospective on Eremenko and Lyubich's entire functions

Related

• A survey on permutable transcendental entire functions and their dynamics
• The dynamics of semigroups of transcendental entire functions II
• On escaping sets of some families of entire functions and dynamics of composite entire functions
• Results on escaping set of an entire function and its composition
• Infinite-dimensional Thurston theory and transcendental dynamics II: classification of entire functions with escaping singular orbits