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The growth rate of an entire function and the Hausdorff dimension of its Julia set

Bergweiler, Walter; Karpińska, Boguslawa and Stallard, Gwyneth M. (2009). The growth rate of an entire function and the Hausdorff dimension of its Julia set. Journal of the London Mathematical Society, 80(3) pp. 680–698.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1112/jlms/jdp042
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Abstract

Let f be a transcendental entire function in the Eremenko-Lyubich class B. We give a lower bound for the Hausdorff dimension of the Julia set of f that depends on the growth of f. This estimate is best possible and is obtained by proving a more general result concerning the size of the escaping set of a function with a logarithmic tract.

Item Type: Journal Article
Copyright Holders: 2009 London Mathematical Society
ISSN: 1469-7750
Project Funding Details:
Funded Project NameProject IDFunding Body
Not SetNot Setthe EU Research Training Network CODY
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 23951
Depositing User: Gwyneth Stallard
Date Deposited: 20 Oct 2010 11:40
Last Modified: 10 Dec 2012 17:26
URI: http://oro.open.ac.uk/id/eprint/23951
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