The Hausdorff Dimension of Julia Sets of Entire Functions IV |
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| Authors: | Stallard Gwyneth M |
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| Institution: | Department of Pure Mathematics, Open University Walton Hall, Milton Keynes, MK7 6AA G.M.Stallard{at}open.ac.uk |
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| Abstract: | It is known that, for a transcendental entire function f, theHausdorff dimension of J(f) satisfies 1  dimJ(f) 2. For eachd  (1, 2), an example of a transcendental entire function fwith dimJ(f) = d is given. It is then indicated how this functioncan be modified to produce a transcendental meromorphic functionF with one pole with dimJ(F) = d. These appear to be the firstexamples of Julia sets with non-integer dimensions whose dimensionshave been calculated exactly. |
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