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THE HAUSDORFF DIMENSION OF JULIA SETS OF ENTIRE FUNCTIONS IV

Published online by Cambridge University Press:  01 April 2000

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

It is known that, for a transcendental entire function f, the Hausdorff dimension of J(f) satisfies 1 [les ] dimJ(f) [les ] 2. For each d ∈ (1, 2), an example of a transcendental entire function f with dimJ(f) = d is given. It is then indicated how this function can be modified to produce a transcendental meromorphic function F with one pole with dimJ(F) = d. These appear to be the first examples of Julia sets with non-integer dimensions whose dimensions have been calculated exactly.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 61 , Issue 2 , April 2000 , pp. 471 - 488
Copyright
The London Mathematical Society 2000

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