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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

Families of Baker domains II


Authors: P. J. Rippon and G. M. Stallard
Journal: Conform. Geom. Dyn. 3 (1999), 67-78
MSC (1991): Primary 30D05; Secondary 58F08
Published electronically: June 14, 1999
MathSciNet review: 1689255
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Abstract: Let $f$ be a transcendental meromorphic function and $U$ be an invariant Baker domain of $f$. We use estimates for the hyperbolic metric to show that there is a relationship between the size of $U$ and the proximity of $f$ in $U$ to the identity function, and illustrate this by discussing how the dynamics of transcendental entire functions of the following form vary with the parameter $a$:

\begin{equation*}f(z) = az + bz^ke^{-z}(1+o(1)) \; \text{ as } \Re (z) \rightarrow \infty, \end{equation*}

where $k \in \mathbf N$, $a \geq 1$ and $b > 0$.


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Additional Information

P. J. Rippon
Affiliation: Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA England
Email: p.j.rippon@open.ac.uk

G. M. Stallard
Affiliation: Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA England
Email: g.m.stallard@open.ac.uk

DOI: http://dx.doi.org/10.1090/S1088-4173-99-00045-4
PII: S 1088-4173(99)00045-4
Received by editor(s): January 5, 1999
Received by editor(s) in revised form: April 19, 1999
Published electronically: June 14, 1999
Article copyright: © Copyright 1999 American Mathematical Society