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Boundaries of escaping Fatou components

Rippon, P. J. and Stallard, G. M. (2011). Boundaries of escaping Fatou components. Proceedings of the American Mathematical Society, 139(8) pp. 2807–2820.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1090/S0002-9939-2011-10842-6
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Abstract

Let $f$ be a transcendental entire function and $U$ be a Fatou component of $f$. We show that if $U$ is an escaping wandering domain of $f$, then most boundary points of $U$ (in the sense of harmonic measure) are also escaping. In the other direction we show that if enough boundary points of $U$ are escaping, then $U$ is an escaping Fatou component. Some applications of these results are given; for example, if $I(f)$ is the escaping set of $f$, then $I(f)\cup\{\infty\}$ is connected.

Item Type: Journal Article
Copyright Holders: 2011 American Mathematical Society
ISSN: 1088-6826
Project Funding Details:
Funded Project NameProject IDFunding Body
Baker's conjecture and Eremenko's conjecture: a unified approach.EP/H006591/1EPSRC (Engineering and Physical Sciences Research Council)
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 30393
Depositing User: Philip Rippon
Date Deposited: 17 Jan 2012 11:15
Last Modified: 24 Mar 2014 14:37
URI: http://oro.open.ac.uk/id/eprint/30393
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