## 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 $b > 0$.## References

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## Bibliographic 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
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1689255