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.

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DOI (Digital Object Identifier) Link:	http://dx.doi.org/doi: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
Funders:	the 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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