On a family of rational perturbations of the doubling map

The goal of this paper is to investigate the parameter plane of a rational family of perturbations of the doubling map given by the Blaschke products $B_a(z)=z^3\frac{z-a}{1-\bar{a}z}$. First we study the basic properties of these maps such as the connectivity of the Julia set as a function of the p...

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Detalles Bibliográficos
Autores: Canela Sánchez, Jordi, Fagella Rabionet, Núria, Garijo Real, Antonio
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2015
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/67324
Acceso en línea:https://hdl.handle.net/2445/67324
Access Level:acceso abierto
Palabra clave:Sistemes dinàmics diferenciables
Funcions de variables complexes
Dinàmica topològica
Fractals
Differentiable dynamical systems
Functions of complex variables
Topological dynamics
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spelling On a family of rational perturbations of the doubling mapCanela Sánchez, JordiFagella Rabionet, NúriaGarijo Real, AntonioSistemes dinàmics diferenciablesFuncions de variables complexesDinàmica topològicaFractalsDifferentiable dynamical systemsFunctions of complex variablesTopological dynamicsFractalsThe goal of this paper is to investigate the parameter plane of a rational family of perturbations of the doubling map given by the Blaschke products $B_a(z)=z^3\frac{z-a}{1-\bar{a}z}$. First we study the basic properties of these maps such as the connectivity of the Julia set as a function of the parameter $a$. We use techniques of quasiconformal surgery to explore the relation between certain members of the family and the degree 4 polynomials $\left(\overline{\overline{z}^2+c}\right)^2+c$. In parameter space, we classify the different hyperbolic components according to the critical orbits and we show how to parametrize those of disjoint type.Taylor and Francis2015info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/67324Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: http://dx.doi.org/10.1080/10236198.2015.1050387Journal of Difference Equations and Applications, 2015, vol. 21, num. 8, p. 715-741http://dx.doi.org/10.1080/10236198.2015.1050387(c) Taylor and Francis, 2015info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/673242026-05-27T06:46:51Z
dc.title.none.fl_str_mv On a family of rational perturbations of the doubling map
title On a family of rational perturbations of the doubling map
spellingShingle On a family of rational perturbations of the doubling map
Canela Sánchez, Jordi
Sistemes dinàmics diferenciables
Funcions de variables complexes
Dinàmica topològica
Fractals
Differentiable dynamical systems
Functions of complex variables
Topological dynamics
Fractals
title_short On a family of rational perturbations of the doubling map
title_full On a family of rational perturbations of the doubling map
title_fullStr On a family of rational perturbations of the doubling map
title_full_unstemmed On a family of rational perturbations of the doubling map
title_sort On a family of rational perturbations of the doubling map
dc.creator.none.fl_str_mv Canela Sánchez, Jordi
Fagella Rabionet, Núria
Garijo Real, Antonio
author Canela Sánchez, Jordi
author_facet Canela Sánchez, Jordi
Fagella Rabionet, Núria
Garijo Real, Antonio
author_role author
author2 Fagella Rabionet, Núria
Garijo Real, Antonio
author2_role author
author
dc.subject.none.fl_str_mv Sistemes dinàmics diferenciables
Funcions de variables complexes
Dinàmica topològica
Fractals
Differentiable dynamical systems
Functions of complex variables
Topological dynamics
Fractals
topic Sistemes dinàmics diferenciables
Funcions de variables complexes
Dinàmica topològica
Fractals
Differentiable dynamical systems
Functions of complex variables
Topological dynamics
Fractals
description The goal of this paper is to investigate the parameter plane of a rational family of perturbations of the doubling map given by the Blaschke products $B_a(z)=z^3\frac{z-a}{1-\bar{a}z}$. First we study the basic properties of these maps such as the connectivity of the Julia set as a function of the parameter $a$. We use techniques of quasiconformal surgery to explore the relation between certain members of the family and the degree 4 polynomials $\left(\overline{\overline{z}^2+c}\right)^2+c$. In parameter space, we classify the different hyperbolic components according to the critical orbits and we show how to parametrize those of disjoint type.
publishDate 2015
dc.date.none.fl_str_mv 2015
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/67324
url https://hdl.handle.net/2445/67324
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: http://dx.doi.org/10.1080/10236198.2015.1050387
Journal of Difference Equations and Applications, 2015, vol. 21, num. 8, p. 715-741
http://dx.doi.org/10.1080/10236198.2015.1050387
dc.rights.none.fl_str_mv (c) Taylor and Francis, 2015
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Taylor and Francis, 2015
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Taylor and Francis
publisher.none.fl_str_mv Taylor and Francis
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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