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Permutable entire functions and multiply connected wandering domains

Benini, Anna Miriam; Rippon, Philip J. and Stallard, Gwyneth M. (2016). Permutable entire functions and multiply connected wandering domains. Advances in Mathematics, 287 pp. 451–462.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1016/j.aim.2015.04.031
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Abstract

Let f and g be permutable transcendental entire functions. We use a recent analysis of the dynamical behaviour in multiply connected wandering domains to make progress on the long standing conjecture that the Julia sets of f and g are equal; in particular, we show that J(f)=J(g) provided that neither f nor g has a simply connected wandering domain in the fast escaping set.

Item Type: Journal Item
Copyright Holders: 2015 Elsevier Inc.
ISSN: 1090-2082
Project Funding Details:
Funded Project NameProject IDFunding Body
Bakers Conjecture and Eremenko's Conjecture: New Directions (XM-12-066-GS)EP/K031163/1EPSRC (Engineering and Physical Sciences Research Council)
Keywords: transcendental entire function; Julia set; permutable functions; multiply connected wandering domain; fast escaping set
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 44549
Depositing User: Philip Rippon
Date Deposited: 12 Oct 2015 10:15
Last Modified: 23 May 2019 16:24
URI: http://oro.open.ac.uk/id/eprint/44549
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