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THE HAUSDORFF DIMENSION OF JULIA SETS OF MEROMORPHIC FUNCTIONS II

Published online by Cambridge University Press:  01 December 1999

GWYNETH M. STALLARD
GWYNETH M. STALLARD
Affiliation:
Department of Pure Mathematics, Open University, Walton Hall, Milton Keynes MK7 6AA
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Abstract

A family of transcendental meromorphic functions, fp(z), p ∈ N is considered. It is shown that, if p [ges ] 6, then the Hausdorff dimension of the Julia set of λfp satisfies dim J(λfp) [les ] 1/p, for 0 < λ < 1/6p, and dim J(λfp) [ges ] 1−(30 ln ln p/ln p), for p4p−1/105 ln p < λ < p4p−1/104 ln p. These results are used elsewhere to show that, for each d ∈ (0, 1), there exists a transcendental meromorphic function for which dim J(f) = d.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 60 , Issue 3 , December 1999 , pp. 847 - 859
Copyright
The London Mathematical Society 1999

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