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Semi-Groups of Analytic Functions that Contain the Identity Map

Semi-Groups of Analytic Functions that Contain the Identity Map We study the behaviour of repeated compositions of different analytic functions taken from a family ${\cal F}$ that only contain self-maps of a hyperbolic subdomain of ℂ. We generalize a result of A. F. Beardon to the case where the closure of the semi-group ${\cal F}_{0}$ , consisting of all finite compositions of functions chosen from family ${\cal F}$ , can contain the identity map. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Semi-Groups of Analytic Functions that Contain the Identity Map

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Publisher
Springer Journals
Copyright
Copyright © 2007 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321642
Publisher site
See Article on Publisher Site

Abstract

We study the behaviour of repeated compositions of different analytic functions taken from a family ${\cal F}$ that only contain self-maps of a hyperbolic subdomain of ℂ. We generalize a result of A. F. Beardon to the case where the closure of the semi-group ${\cal F}_{0}$ , consisting of all finite compositions of functions chosen from family ${\cal F}$ , can contain the identity map.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Jan 19, 2007

References