Singular orbits and Baker domains

Rempe, Lasse ORCID: 0000-0001-8032-8580 Singular orbits and Baker domains.

Text 2009.07020v1.pdf - Submitted version Download (339kB) | Preview

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:	7 pages
Uncontrolled Keywords:	math.DS, math.DS, math.CV, 37F10 (primary), 30D05, 37F31 (secondary)
Depositing User:	Symplectic Admin
Date Deposited:	28 Sep 2020 08:04
Last Modified:	18 Jan 2023 23:31
Related URLs:	Author
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3102573

Available Versions of this Item

• Singular orbits and Baker domains. (deposited 28 Sep 2020 08:04) [Currently Displayed]
  • Singular orbits and Baker domains. (deposited 02 Dec 2020 15:01)