The Open UniversitySkip to content
 

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://doi.org/10.1017/S0143385706000162
Google Scholar: Look up in Google Scholar

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
Mathematics, Computing and Technology
Item ID: 7817
Depositing User: Philip Rippon
Date Deposited: 25 May 2007
Last Modified: 14 Jan 2016 16:32
URI: http://oro.open.ac.uk/id/eprint/7817
Share this page:

Altmetrics

Scopus Citations

▼ Automated document suggestions from open access sources

Actions (login may be required)

Policies | Disclaimer

© The Open University   + 44 (0)870 333 4340   general-enquiries@open.ac.uk