Hausdorff dimensions of escaping sets of transcendental entire functions

Rempe, Lasse and Stallard, Gwyneth M. (2010). Hausdorff dimensions of escaping sets of transcendental entire functions. Proceedings of the American Mathematical Society, 138(5) pp. 1657–1665.

URL: http://www.ams.org/journals/proc/2010-138-05/S0002...

Abstract

Suppose that f and g are transcendental entire functions, each with a bounded set of singular values, and that f and g are affinely equivalent. We show that the escaping sets of f and g have the same Hausdorff dimension. Using a result of the second author, we deduce that there exists a family of transcendental entire functions for which the escaping set has Hausdorff dimension equal to one.

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About

• Item ORO ID
• 23953
• Item Type
• Journal Item
• ISSN
• 1088-6826
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Not Set	Not Set	the European CODY network

• 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 American Mathematical Society
• Depositing User
• Gwyneth Stallard