Hyperbolic dimension and radial Julia sets of transcendental functions
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- by Lasse Rempe
- Proc. Amer. Math. Soc. 137 (2009), 1411-1420
- DOI: https://doi.org/10.1090/S0002-9939-08-09650-0
- Published electronically: November 3, 2008
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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.References
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Bibliographic Information
- Lasse Rempe
- Affiliation: Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom
- MR Author ID: 738017
- ORCID: 0000-0001-8032-8580
- Email: l.rempe@liverpool.ac.uk
- 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
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 1411-1420
- MSC (2000): Primary 37F35; Secondary 37F10, 30D05
- DOI: https://doi.org/10.1090/S0002-9939-08-09650-0
- MathSciNet review: 2465667