Functions of genus zero for which the fast escaping set has Hausdorff dimension two
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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.References
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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
- MR Author ID: 952973
- Email: david.sixsmith@open.ac.uk
- 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
- © Copyright 2015 American Mathematical Society
- 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
- MathSciNet review: 3326040