Rempe, Lasse and Stallard, Gwyneth M.
(2010).
| URL: | http://www.ams.org/journals/proc/2010-138-05/S0002... |
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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.
| Item Type: | Article | ||||||
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| Copyright Holders: | 2009 American Mathematical Society | ||||||
| ISSN: | 1088-6826 | ||||||
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| Academic Unit/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |
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| Item ID: | 23953 | ||||||
| Depositing User: | Gwyneth Stallard | ||||||
| Date Deposited: | 20 Oct 2010 11:02 | ||||||
| Last Modified: | 04 Oct 2016 10:47 | ||||||
| URI: | http://oro.open.ac.uk/id/eprint/23953 | ||||||
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