Families of Baker domains II

Rippon, P.; Stallard, G.

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

Families of Baker domains II
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by P. J. Rippon and G. M. Stallard

Conform. Geom. Dyn. 3 (1999), 67-78

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

Published electronically: June 14, 1999

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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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