Baker domains of meromorphic functions

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

DOI (Digital Object Identifier) Link:	http://dx.doi.org/doi:10.1017/S0143385706000162
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Abstract

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
URI:	http://oro.open.ac.uk/id/eprint/7817

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