Conformal Geometry and Dynamics

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ISSN 1088-4173

Families of Baker domains II

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

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

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

References:

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