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The growth rate of an entire function and the Hausdorff dimension of its Julia set

Let f be a transcendental entire function in the Eremenko-Lyubich class B. We give a lower bound for the Hausdorff dimension of the Julia set of f that depends on the growth of f. This estimate is best possible and is obtained by proving a more general result concerning the size of the escaping set of a function with a logarithmic tract.

preprint2008arXivOpen access
Walter BergweilerBogusława KarpińskaGwyneth M. Stallard
math.CVmath.DS
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Walter BergweilerBogusława KarpińskaGwyneth M. Stallard

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