Families of Baker domains II

Rippon, P.; Stallard, G.

doi:10.1090/S1088-4173-99-00045-4

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 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 .

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