Bergweiler, W.; Rippon, Philip J. and Stallard, Gwyneth M.
(2008).
Dynamics of meromorphic functions with direct or logarithmic singularities.
Proceedings of the London Mathematical Society, 97(2) pp. 368–400.
Abstract
Let f be a transcendental meromorphic function and denote by J(f) the Julia set and by I(f) the escaping set. We show that if f has a direct singularity over infinity, then I(f) has an unbounded component and I(f)∩J(f) contains continua. Moreover, under this hypothesis I(f)∩J(f) has an unbounded component if and only if f has no Baker wandering domain. If f has a logarithmic singularity over infinity, then the upper box dimension of I(f)∩J(f) is 2 and the Hausdorff dimension of J(f) is strictly greater than 1. The above theorems are deduced from more general results concerning functions which have ‘direct or logarithmic tracts’, but which need not be meromorphic in the plane. These results are obtained by using a generalization of Wiman–Valiron theory. This method is also applied to complex differential equations.
Item Type: 
Journal Article

ISSN: 
1460244X 
Project Funding Details: 
Funded Project Name  Project ID  Funding Body 

Not Set  Not Set  London Mathematical Society  Not Set  Not Set  German–Israeli Foundation for Scientific Research and Development [grant number G809234.6/2003]  Not Set  Not Set  EU Research Training Network  Not Set  Not Set  ESF Research Networking Programme 

Academic Unit/Department: 
Mathematics, Computing and Technology > Mathematics and Statistics 
Item ID: 
15753 
Depositing User: 
Colin Smith

Date Deposited: 
14 Apr 2009 20:29 
Last Modified: 
02 Dec 2010 20:26 
URI: 
http://oro.open.ac.uk/id/eprint/15753 
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