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THE HAUSDORFF DIMENSION OF JULIA SETS OF ENTIRE FUNCTIONS IV

  • GWYNETH M. STALLARD (a1)

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.

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THE HAUSDORFF DIMENSION OF JULIA SETS OF ENTIRE FUNCTIONS IV

  • GWYNETH M. STALLARD (a1)

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