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Baker domains of meromorphic functions

Rippon, P.J. (2006). Baker domains of meromorphic functions. Ergodic Theory and Dynamical Systems, 26(4) pp. 1225–1233.

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Let $f$ be a transcendental meromorphic function and $U$ be an invariant Baker domain of $f$. We obtain a new estimate for the growth of the iterates of $f$ in $U$, and we use this estimate to improve an earlier result relating the geometric properties of $U$ and the proximity of $f$ in $U$ to the identity function. We illustrate the latter result by considering transcendental meromorphic functions $f$ of the form
$ f(z) = az + bz^ke^{-z}(1+o(1)) \; \mbox{ as } \Re (z) \rightarrow \infty, $
where $k \in \bf N$, $a > 1$ and $b > 0$, and we show that these functions have Baker domains which contain an unbounded set of critical points and an unbounded set of critical values.

Item Type: Journal Article
ISSN: 0143-3857
Extra Information: Some of the symbols may not have transferred correctly into this bibliographic record and/or abstract.
Keywords: Baker domain; meromorphic function;
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 7817
Depositing User: Philip Rippon
Date Deposited: 25 May 2007
Last Modified: 02 Dec 2010 19:59
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