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

DOI:
https://doi.org/10.1090/S1088-4173-99-00045-4

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

MR Author ID:
190595

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

MR Author ID:
292621

Email:
g.m.stallard@open.ac.uk

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