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DIMENSIONS OF JULIA SETS OF HYPERBOLIC MEROMORPHIC FUNCTIONS

Published online by Cambridge University Press:  28 November 2001

GWYNETH M. STALLARD
GWYNETH M. STALLARD
Affiliation:
Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA; g.m.stallard@open.ac.uk
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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).

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 6 , November 2001 , pp. 689 - 694
Copyright
© The London Mathematical Society 2001

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