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


Author: D. J. Sixsmith
Journal: Proc. Amer. Math. Soc. 143 (2015), 2597-2612
MSC (2010): Primary 37F10; Secondary 30D05
DOI: https://doi.org/10.1090/S0002-9939-2015-12487-2
Published electronically: February 17, 2015
MathSciNet review: 3326040
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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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Additional Information

D. J. Sixsmith
Affiliation: Department of Mathematics and Statistics, Walton Hall, The Open University, Milton Keynes MK7 6AA, United Kingdom
Email: david.sixsmith@open.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-2015-12487-2
Received by editor(s): November 27, 2013
Received by editor(s) in revised form: February 6, 2014
Published electronically: February 17, 2015
Additional Notes: The author was supported by Engineering and Physical Sciences Research Council grant EP/J022160/1.
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2015 American Mathematical Society