Dimensions of Julia sets of meromorphic functions with finitely many poles

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.