Unbounded fast escaping wandering domains

Vasiliki Evdoridou*, Adi Glücksam, Leticia Pardo-Simón

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We introduce a new approximation technique into the context of complex dynamics that allows us to construct examples of transcendental entire functions with unbounded wandering domains. We provide examples of entire functions with an orbit of unbounded fast escaping wandering domains, answering a question of Rippon and Stallard. Moreover, these examples cover all possible types of simply-connected wandering domains in terms of convergence to the boundary. In relation to a conjecture of Baker, it was unknown whether functions of order less than one could have unbounded wandering domains. For any given order greater than 1/2 and smaller than 1, we provide an entire function of such order with an unbounded wandering domain.

Original languageEnglish (US)
Article number108914
JournalAdvances in Mathematics
StatePublished - Mar 15 2023


  • Entire functions
  • Fast escaping set
  • Wandering domains

ASJC Scopus subject areas

  • General Mathematics


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