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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DOI (Digital Object Identifier) Link:	http://dx.doi.org/doi: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
Funders:	EPSRC grant EP/H006591/1
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:	05 Dec 2012 15:43
URI:	http://oro.open.ac.uk/id/eprint/30393

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