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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.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1112/plms/pds001
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Abstract

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 Article
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/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Related URLs:
Item ID: 31138
Depositing User: Philip Rippon
Date Deposited: 17 Jan 2012 12:01
Last Modified: 26 Jun 2013 15:21
URI: http://oro.open.ac.uk/id/eprint/31138
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