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Dimensions of Julia sets of meromorphic functions with finitely many poles

Rippon, P.J. and Stallard, G.M. (2006). Dimensions of Julia sets of meromorphic functions with finitely many poles. Ergodic Theory and Dynamical Systems, 26(02) pp. 525–538.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1017/S0143385705000544
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Abstract

Let $f$ be a transcendental meromorphic function with finitely many poles such that the finite singularities of $f^{-1}$ lie in a bounded set. We show that the Julia set of $f$ has Hausdorff dimension strictly greater than one and packing dimension equal to two. The proof for Hausdorff dimension simplifies the earlier argument given for transcendental entire functions.

Item Type: Journal Article
ISSN: 1469-4417
Extra Information: Some of the symbols may not have transferred correctly into this bibliographic record and/or abstract.
Keywords: dimensions; Julia sets
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 3846
Depositing User: Gwyneth Stallard
Date Deposited: 09 Mar 2007
Last Modified: 02 Dec 2010 19:50
URI: http://oro.open.ac.uk/id/eprint/3846
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