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

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

2008-07-15

arxiv.org/abs/0807.2363v1

J. London Math. Soc. 80 (2009), 680-698

Mathematics

Complex Variables

19 pages

Scientific paper

10.1112/jlms/jdp042

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.

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