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Fast escaping points of entire functions

Rippon, Philip and Stallard, Gwyneth (2012). Fast escaping points of entire functions. Proceedings of the London Mathematical Society, 105(4) pp. 787–820.

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Let $f$ be a transcendental entire function and let $A(f)$ denote the set of points that escape to infinity `as fast as possible’ under iteration. By writing $A(f)$ as a countable union of closed sets, called `levels’ of $A(f)$, we obtain a new understanding of the structure of this set. For example, we show that if $U$ is a Fatou component in $A(f)$, then $\partial U\subset A(f)$ and this leads to significant new results and considerable improvements to existing results about $A(f)$. In particular, we study functions for which $A(f)$, and each of its levels, has the structure of an `infinite spider's web’. We show that there are many such functions and that they have a number of strong dynamical properties. This new structure provides an unexpected connection between a conjecture of Baker concerning the components of the Fatou set and a conjecture of Eremenko concerning the components of the escaping set.

Item Type: Journal Item
Copyright Holders: 2012 London Mathematical Society
ISSN: 1460-244X
Project Funding Details:
Funded Project NameProject IDFunding Body
Not SetNot SetEPSRC (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)
Related URLs:
Item ID: 31138
Depositing User: Philip Rippon
Date Deposited: 17 Jan 2012 12:01
Last Modified: 07 Dec 2018 09:59
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