Dimensions of Julia sets of hyperbolic meromorphic functions

Stallard, Gwyneth M. (2001). Dimensions of Julia sets of hyperbolic meromorphic functions. Bulletin of the London Mathematical Society, 33(6) pp. 689–694.

DOI: https://doi.org/10.1112/S0024609301008426

URL: http://journals.cambridge.org/action/displayIssue?...

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. In this paper it is shown that, for a hyperbolic transcendental meromorphic function $f$, the packing and upper box dimensions of $J(f)$ are equal, but can be strictly greater than the Hausdorff dimension of $J(f)$.

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