Singular orbits and Baker domains



Rempe, Lasse ORCID: 0000-0001-8032-8580
(2022) Singular orbits and Baker domains. MATHEMATISCHE ANNALEN, 382 (3-4). pp. 1475-1483.

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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 Mihaljevi\'c and the author from 2013, and complements recent work of Bara\'nski et al concerning this question.

Item Type: Article
Additional Information: 8 pages; to appear in Mathematische Annalen. V2: Minor revisions, changes and corrections
Uncontrolled Keywords: math.DS, math.DS, math.CV, 37F10 (primary), 30D05, 37F31 (secondary)
Depositing User: Symplectic Admin
Date Deposited: 02 Dec 2020 15:01
Last Modified: 18 Jan 2023 23:19
DOI: 10.1007/s00208-020-02132-z
Open Access URL: https://doi.org/10.1007/s00208-020-02132-z
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3108904

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