Nieminen , P J & Gallardo-Gutiérrez , E A 2015 , ' The Linear Fractional Model Theorem and Aleksandrov-Clark measures ' , Journal of the London Mathematical Society , vol. 91 , no. 2 , pp. 596-608 . https://doi.org/10.1112/jlms/jdv002
Title: | The Linear Fractional Model Theorem and Aleksandrov-Clark measures |
Author: | Nieminen, Pekka J.; Gallardo-Gutiérrez, Eva A. |
Contributor organization: | Department of Mathematics and Statistics |
Date: | 2015 |
Language: | eng |
Number of pages: | 13 |
Belongs to series: | Journal of the London Mathematical Society |
ISSN: | 0024-6107 |
DOI: | https://doi.org/10.1112/jlms/jdv002 |
URI: | http://hdl.handle.net/10138/155184 |
Abstract: | A remarkable result by Denjoy and Wolff states that every analytic self-map. of the open unit disc D of the complex plane, except an elliptic automorphism, has an attractive fixed point to which the sequence of iterates {phi(n)}(n >= 1) converges uniformly on compact sets: if there is no fixed point in D, then there is a unique boundary fixed point that does the job, called the Denjoy-Wolff point. This point provides a classification of the analytic self-maps of D into four types: maps with interior fixed point, hyperbolic maps, parabolic automorphism maps and parabolic non-automorphism maps. We determine the convergence of the Aleksandrov-Clark measures associated to maps falling in each group of such classification. |
Subject: | 111 Mathematics |
Peer reviewed: | Yes |
Usage restriction: | openAccess |
Self-archived version: | publishedVersion |
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