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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.

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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 Item
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/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 30393
Depositing User: Philip Rippon
Date Deposited: 17 Jan 2012 11:15
Last Modified: 07 Dec 2018 09:57
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