Rippon, P. J. and Stallard, G. M.
(2008).
*Journal of the London Mathematical Society*, 77(2) pp. 405–423.

DOI (Digital Object Identifier) Link: | https://doi.org/10.1112/jlms/jdm118 |
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Google Scholar: | Look up in Google Scholar |

## Abstract

We describe conditions under which a multiply connected wandering domain of a transcendental meromorphic function with a finite number of poles must be a Baker wandering domain, and we discuss the possible eventual connectivity of Fatou components of transcendental meromorphic functions. We also show that if *f* is meromorphic, *U* is a bounded component of *F*(*f*) and *V* is the component of *F*(*f*) such that *F*(*U*) is contained in *V*, then f maps each component of the boundary of *U* onto a component of the boundary of *V* in C^. We give examples which show that our results are sharp; for example, we prove that a multiply connected wandering domain can map to a simply connected wandering domain, and vice versa.

Item Type: | Journal Item |
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Copyright Holders: | 2008 The London Mathematical Society |

ISSN: | 1469-7750 |

Academic Unit/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |

Item ID: | 22450 |

Depositing User: | Philip Rippon |

Date Deposited: | 28 Jul 2010 15:22 |

Last Modified: | 04 Oct 2016 10:41 |

URI: | http://oro.open.ac.uk/id/eprint/22450 |

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