Functions of genus zero for which the fast escaping set has Hausdorff dimension two

Sixsmith, D. J. (2015). Functions of genus zero for which the fast escaping set has Hausdorff dimension two. Proceedings of the American Mathematical Society, 143(6) pp. 2597–2612.

DOI: https://doi.org/10.1090/S0002-9939-2015-12487-2

Abstract

We study a family of transcendental entire functions of genus zero, for which all of the zeros lie within a closed sector strictly smaller than a half-plane. In general these functions lie outside the Eremenko-Lyubich class. We show that for functions in this family the fast escaping set has Hausdorff dimension equal to two.

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About

• Item ORO ID
• 39716
• Item Type
• Journal Item
• ISSN
• 1088-6826
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Dimensions in complex dynamics: spiders' webs and speed of escape	EP/J022160/1	EPSRC (Engineering and Physical Sciences Research Council)

• 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
• © 2015 American Mathematical Society
• Depositing User
• Dave Sixsmith