Oscillating Wandering Domains for Functions with Escaping Singular Values

Abstract

We construct a transcendental entire $f:\mathbb{C}\to \mathbb{C}$ such that (1) $f$ has bounded singular set, (2) $f$ has a wandering domain, and (3) each singular value of $f$ escapes to infinity under iteration by $f$.

arXiv commentThis version incorporates referee comments, and contains significant expository improvements

References in corpus (4)

• Fatou components and singularities of meromorphic functions
• Wandering domains for entire functions of finite order in the Eremenko-Lyubich class
• On the set where the iterates of an entire function are neither escaping nor bounded
• Absence of wandering domains for some real entire functions with bounded singular sets

Cited by in corpus (1)

• The escaping set in transcendental dynamics