Stallard, Gwyneth M.
Dimensions of Julia sets of hyperbolic entire functions.
Bulletin of the London Mathematical Society, 36(2) pp. 263–270.
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.
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