The Linear Fractional Model Theorem and Aleksandrov-Clark measures

dc.contributor.authorGallardo Gutiérrez, Eva A.
dc.contributor.authorNieminen, Pekka J.
dc.description.abstractA 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
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.sponsorshipMinisterio de Ciencia e Innovación (MICINN)
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dc.journal.titleJournal of the London Mathematical Society. Second Series
dc.publisherOxford University Press
dc.rights.accessRightsrestricted access
dc.subject.keywordUnit disk
dc.subject.ucmAnálisis matemático
dc.subject.unesco1202 Análisis y Análisis Funcional
dc.titleThe Linear Fractional Model Theorem and Aleksandrov-Clark measures
dc.typejournal article
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