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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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