Dimensions of Julia sets of meromorphic functions with finitely many poles

Rippon, P.J. and Stallard, G.M. (2006). Dimensions of Julia sets of meromorphic functions with finitely many poles. Ergodic Theory and Dynamical Systems, 26(02) pp. 525–538.

DOI: https://doi.org/10.1017/S0143385705000544

Abstract

Let $f$ be a transcendental meromorphic function with finitely many poles such that the finite singularities of $f^{-1}$ lie in a bounded set. We show that the Julia set of $f$ has Hausdorff dimension strictly greater than one and packing dimension equal to two. The proof for Hausdorff dimension simplifies the earlier argument given for transcendental entire functions.

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