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Baker's conjecture and Eremenko's conjecture for functions with negative zeros

Rippon, Philip and Stallard, Gwyneth (2012). Baker's conjecture and Eremenko's conjecture for functions with negative zeros. Journal d'Analyse Mathematique, 120(1) pp. 291–309.

URL: http://www.springer.com/mathematics/analysis/journ...
DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1007/s11854-013-0021-2
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Abstract

We introduce a new technique that allows us to make progress on two long standing conjectures in transcendental dynamics: Baker's conjecture that a transcendental entire function of order less than ½ has no unbounded Fatou components, and Eremenko's conjecture that all the components of the escaping set of an entire function are unbounded. We show that both conjectures hold for many transcendental entire fuctions whose zeros all lie on the negative real axis, in particular those of order less than ½. Our proofs use a classical distortion theorem based on contraction of the hyperbolic metric, together with new results which show that the images of certain curves must wind many times round the origin.

Item Type: Journal Article
Copyright Holders: 2012 Springer
ISSN: 0021-7670
Project Funding Details:
Funded Project NameProject IDFunding Body
Not SetEP/H006591/1EPSRC (Engineering and Physical Sciences Research Council)
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Related URLs:
Item ID: 31617
Depositing User: Philip Rippon
Date Deposited: 17 Jan 2012 11:53
Last Modified: 12 Sep 2013 08:30
URI: http://oro.open.ac.uk/id/eprint/31617
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