Ergodic Theory and Dynamical Systems



Dimensions of Julia sets of meromorphic functions with finitely many poles


P. J. RIPPON a1 and G. M. STALLARD a1
a1 Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK (e-mail: p.j.rippon@open.ac.uk, g.m.stallard@open.ac.uk)

Article author query
rippon pj   [Google Scholar] 
stallard gm   [Google Scholar] 
 

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.

(Published Online January 18 2006)
(Received February 10 2005)
(Revised October 4 2005)