Gallardo Gutiérrez, Eva AntoniaNieminen, Pekka J.2023-06-192023-06-192015Gallardo Gutiérrez, E. A. & Nieminen, P. J. «The Linear Fractional Model Theorem and Aleksandrov-Clark Measures». Journal of the London Mathematical Society, vol. 91, n.o 2, abril de 2015, pp. 596-608. DOI.org (Crossref), https://doi.org/10.1112/jlms/jdv002.0024-610710.1112/jlms/jdv002https://hdl.handle.net/20.500.14352/34941A 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 classificationengjournal articlehttps//doi.org/10.1112/jlms/jdv002http://jlms.oxfordjournals.org/content/91/2/596.abstractrestricted access517Analytic-FunctionsUnit diskIterationAnálisis matemático1202 Análisis y Análisis Funcional