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Dimensions of Julia sets of meromorphic functions with finitely many poles

Published online by Cambridge University Press:  18 January 2006

P. J. RIPPON  and
G. M. STALLARD
P. J. RIPPON
Affiliation:
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)
G. M. STALLARD
Affiliation:
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)
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 2 , April 2006 , pp. 525 - 538
Copyright
2006 Cambridge University Press

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