Singular orbits and Baker domains

Abstract

We show that there is a transcendental meromorphic function with an invariant Baker domain $U$ such that every singular value of $f$ is a super-attracting periodic point. This answers a question of Bergweiler from 1993. We also show that $U$ can be chosen to contain arbitrarily large round annuli, centred at zero, of definite modulus. This answers a question of Mihaljević and the author from 2013, and complements recent work of Barański et al concerning this question.

8 pages; to appear in Mathematische Annalen. V2: Minor revisions, changes and corrections

References in corpus (2)

• Fatou components and singularities of meromorphic functions
• Absorbing sets and Baker domains for holomorphic maps

Cited by in corpus (2)

• The escaping set in transcendental dynamics
• Invariant escaping Fatou components with two rank 1 limit functions for automorphisms of ${\mathbb{C}}^2$