Stallard, Gwyneth M.
(2004).
| URL: | http://journals.cambridge.org/action/displayAbstra... |
|---|---|
| DOI (Digital Object Identifier) Link: | https://doi.org/10.1112/S0024609303002698 |
| Google Scholar: | Look up in Google Scholar |
Abstract
It is known that, if is a hyperbolic rational function, then the Hausdorff, packing and box dimensions of the Julia set
are equal. It is also known that there is a family of hyperbolic transcendental meromorphic functions with infinitely many poles for which this result fails to be true. In this paper, new methods are used to show that there is a family of hyperbolic transcendental entire functions
,
, such that the box and packing dimensions of
are equal to two, even though as
the Hausdorff dimension of
tends to one, the lowest possible value for the Hausdorff dimension of the Julia set of a transcendental entire function.
| Item Type: | Article |
|---|---|
| ISSN: | 1469-2120 |
| Academic Unit/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |
| Item ID: | 3839 |
| Depositing User: | Gwyneth Stallard |
| Date Deposited: | 30 Jun 2006 |
| Last Modified: | 04 Oct 2016 09:50 |
| URI: | http://oro.open.ac.uk/id/eprint/3839 |
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