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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hyperbolic dimension and radial Julia sets of transcendental functions


Author: Lasse Rempe
Journal: Proc. Amer. Math. Soc. 137 (2009), 1411-1420
MSC (2000): Primary 37F35; Secondary 37F10, 30D05
Published electronically: November 3, 2008
MathSciNet review: 2465667
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Abstract: We survey the definition of the radial Julia set $ J_r(f)$ of a meromorphic function (in fact, more generally, any Ahlfors islands map), and give a simple proof that the Hausdorff dimension of $ J_r(f)$ and the hyperbolic dimension $ \dim_{\operatorname{hyp}}(f)$ always coincide.


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Additional Information

Lasse Rempe
Affiliation: Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom
Email: l.rempe@liverpool.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09650-0
PII: S 0002-9939(08)09650-0
Keywords: Hyperbolic dimension, radial Julia set, iterated function system, entire function, meromorphic function, Ahlfors islands map, Hausdorff dimension, conformal measure
Received by editor(s): December 21, 2007
Received by editor(s) in revised form: May 22, 2008
Published electronically: November 3, 2008
Additional Notes: The author was supported by EPSRC grant EP/E017886/1.
Communicated by: Jane M. Hawkins
Article copyright: © Copyright 2008 American Mathematical Society