On the Hausdorff dimension of the Julia set of a regularly growing entire function
Abstract
We show that if the growth of a transcendental entire function f is sufficiently regular, then the Julia set and the escaping set of f have Hausdorff dimension 2.
- Publication:
-
Mathematical Proceedings of the Cambridge Philosophical Society
- Pub Date:
- January 2010
- DOI:
- 10.1017/S0305004109990491
- arXiv:
- arXiv:0909.3988
- Bibcode:
- 2010MPCPS.148..531B
- Keywords:
-
- Mathematics - Dynamical Systems;
- Mathematics - Complex Variables;
- 37F10;
- 30D05;
- 30D15
- E-Print:
- 21 pages