Singular perturbations of Blaschke products and connectivity of Fatou components
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Título
Singular perturbations of Blaschke products and connectivity of Fatou componentsAutoría
Fecha de publicación
2017Editor
American Institute of Mathematical Sciences (AIMS)ISSN
1078-0947; 1553-5231Cita bibliográfica
Canela Jordi. Singular perturbations of Blaschke products and connectivity of Fatou components. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 3567-3585. doi: 10.3934/dcds.2017153Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://www.aimsciences.org/article/doi/10.3934/dcds.2017153Versión
info:eu-repo/semantics/acceptedVersionPalabras clave / Materias
Resumen
The goal of this paper is to study the family of singular perturbations of Blaschke products given by Ba,λ(z)=z3z−a1−a¯z+λz2. We focus on the study of these rational maps for parameters a in the punctured disk D∗ and ... [+]
The goal of this paper is to study the family of singular perturbations of Blaschke products given by Ba,λ(z)=z3z−a1−a¯z+λz2. We focus on the study of these rational maps for parameters a in the punctured disk D∗ and |λ| small. We prove that, under certain conditions, all Fatou components of a singularly perturbed Blaschke product Ba,λ have finite connectivity but there are components of arbitrarily large connectivity within its dynamical plane. Under the same conditions we prove that the Julia set is the union of countably many Cantor sets of quasicircles and uncountably many point components. [-]
Publicado en
Discrete & Continuous Dynamical Systems - A, 2017, 37 (7).Proyecto de investigación
Grant 346300 for IMPAN from the Simons Foundation and the matching 2015–2019 Polish MNiSW fund, by RedIUM and MINECO (Spain) through the research network MTM2014-55580-REDT, and by the mathematics institute IMACDerechos de acceso
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info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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