Singular orbits and Baker domains
Dynamical Systems
2024-12-10 v2 Complex Variables
Abstract
We show that there is a transcendental meromorphic function with an invariant Baker domain such that every singular value of is a super-attracting periodic point. This answers a question of Bergweiler from 1993. We also show that can be chosen to contain arbitrarily large round annuli, centred at zero, of definite modulus. This answers a question of Mihaljevi\'c and the author from 2013, and complements recent work of Bara\'nski et al concerning this question.
Cite
@article{arxiv.2009.07020,
title = {Singular orbits and Baker domains},
author = {Lasse Rempe},
journal= {arXiv preprint arXiv:2009.07020},
year = {2024}
}
Comments
8 pages; to appear in Mathematische Annalen. V2: Minor revisions, changes and corrections