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The Hausdorff dimension of Julia sets of entire functions III

Published online by Cambridge University Press:  01 September 1997

GWYNETH M. STALLARD
GWYNETH M. STALLARD
Affiliation:
Faulty of Mathematics and Computing, The Open University, Walton Hall, Milton Keynes, MK7 6AA
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Abstract

It is known that, for a transcendental entire function f, the Hausdorff dimension of the Julia set of f satisfies 1[les ]dim J(f)[les ]2. In this paper we introduce a family of transcendental entire functions fp, K for which the set {dim J(fp, K)[ratio ]0<p, K<∞} has infemum 1 and supremum 2.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 122 , Issue 2 , September 1997 , pp. 223 - 244
Copyright
Cambridge Philosophical Society 1997

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