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The Linear Fractional Model Theorem and Aleksandrov-Clark measures

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dc.contributor.authorGallardo Gutiérrez, Eva A.
dc.contributor.authorNieminen, Pekka J.
dc.date.accessioned2023-06-19T14:57:21Z
dc.date.available2023-06-19T14:57:21Z
dc.date.issued2015
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.refereedTRUE
dc.description.sponsorshipMinisterio de Ciencia e Innovación (MICINN)
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/34302
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dc.identifier.doi10.1112/jlms/jdv002
dc.identifier.issn0024-6107
dc.identifier.officialurlhttp://jlms.oxfordjournals.org/content/91/2/596.abstract
dc.identifier.relatedurlhttp://jlms.oxfordjournals.org
dc.identifier.urihttps://hdl.handle.net/20.500.14352/34941
dc.issue.number2
dc.journal.titleJournal of the London Mathematical Society. Second Series
dc.language.isoeng
dc.page.final608
dc.page.initial596
dc.publisherOxford University Press
dc.relation.projectIDMTM2013-42105-P
dc.rights.accessRightsrestricted access
dc.subject.cdu517
dc.subject.keywordAnalytic-Functions
dc.subject.keywordUnit disk
dc.subject.keywordIteration
dc.subject.ucmAnálisis matemático
dc.subject.unesco1202 Análisis y Análisis Funcional
dc.titleThe Linear Fractional Model Theorem and Aleksandrov-Clark measures
dc.typejournal article
dc.volume.number91
dspace.entity.typePublication
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