Computational Methods and Function Theory 7 (2007), No. 1, 239--247
Copyright Heldermann Verlag 2007
Semi-Groups of Analytic Functions that Contain the Identity Map
email@example.com , Saratov State University, Department of Mathematics and Mechanics, Astrakhanskaya Str. 83, 410012 Saratov, Russia.
We study the behaviour of repeated compositions of different analytic functions taken from a family 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 F0, consisting of all finite compositions of functions chosen from family F, can contain the identity map.
Keywords: Compositions of analytic functions, hyperbolic domains, Denjoy-Wolff Theorem, univalent functions, Loewner-Kufarev equation.
MSC 2000: 30D05, 30C35.
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