2- https://doi.org/10.1112/s0024609303002698
DIMENSIONS OF JULIA SETS OF HYPERBOLIC ENTIRE FUNCTIONS
- Feb 2, 2004
- Bulletin of the London Mathematical Society
- Gwyneth M Stallard
Abstract
It is known that, if f is a hyperbolic rational function, then the Hausdorff, packing and box dimensions of the Julia set J(f) 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 fK, K ∈ N, such that the box and packing dimensions of JfK are equal to two, even though as K → ∞ the Hausdorff dimension of JfK tends to one, the lowest possible value for the Hausdorff dimension of the Julia set of a transcendental entire function. 2000 Mathematics Subject Classification 30D05, 37F10, 37F15, 37F35, 37F50.
- # Transcendental Entire Function
- # Packing Dimensions
- # Transcendental Functions
- # Box Dimensions
- # Hausdorff Dimension
- # Hyperbolic Functions
- # Transcendental Function
- # Transcendental Meromorphic Functions
- # Julia Set
- # Meromorphic Functions
