Skip to main content
Article thumbnail
Location of Repository

Dynamics of meromorphic functions with direct or logarithmic singularities

By Walter Bergweiler, Philip J. Rippon and Gwyneth M. Stallard


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

Year: 2008
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.