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.

DOI: https://doi.org/10.1112/jlms/jdp042

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.

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About

• Item ORO ID
• 23951
• Item Type
• Journal Item
• ISSN
• 1469-7750
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Not Set	Not Set	the EU Research Training Network CODY

• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2009 London Mathematical Society
• Depositing User
• Gwyneth Stallard