The Linear Fractional Model Theorem and Aleksandrov-Clark measures

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http://hdl.handle.net/10138/155184

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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: University of Helsinki, 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
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
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