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The Linear Fractional Model Theorem and Aleksandrov-Clark measures

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Gallardo Gutiérrez, Eva A. and Nieminen, Pekka J. (2015) The Linear Fractional Model Theorem and Aleksandrov-Clark measures. Journal of the London Mathematical Society. Second Series, 91 (2). pp. 596-608. ISSN 0024-6107

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Official URL: http://jlms.oxfordjournals.org/content/91/2/596.abstract


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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


Item Type:Article
Uncontrolled Keywords:Analytic-Functions; Unit disk; Iteration
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:34302
Deposited On:01 Dec 2015 08:43
Last Modified:02 Dec 2015 11:28

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