Israel Journal of Mathematics

, Volume 192, Issue 1, pp 449–472 | Cite as

On the packing dimension of the Julia set and the escaping set of an entire function

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Abstract

Let f be a transcendental entire function. We give conditions which imply that the Julia set and the escaping set of f have packing dimension 2. For example, this holds if there exists a positive constant c less than 1 such that the minimum modulus L(r, f) and the maximum modulus M(r, f) satisfy log L(r, f) ≤ c logM(r, f) for large r. The conditions are also satisfied if logM(2r, f) ≥ d logM(r, f) for some constant d greater than 1 and all large r.

Keywords

Entire Function American Mathematical Society Meromorphic Function London Mathematical Society Logarithmic Derivative 
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Copyright information

© Hebrew University Magnes Press 2012

Authors and Affiliations

  1. 1.Mathematisches SeminarChristian-Albrechts-Universität zu KielKielGermany

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