Fractal dimension of the universal Julia sets for the Chebyshev-Halley family of methods

The concept of universal Julia set introduced in [5] allows us to conclude that the dynamics of a root-finding algorithm applied to any quadratic polynomial can be understood through the analysis of a particular rational map. In this study we go a step beyond in this direction. In particular, we can...

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Detalles Bibliográficos
Autores: Gutiérrez, J.M. [0000-0002-0434-7250], Magreñán, Á.A. [0000-0002-6991-5706], Varona, J.L. [0000-0002-2023-9946]
Tipo de recurso: capítulo de libro
Estado:Versión aceptada para publicación
Fecha de publicación:2011
País:España
Institución:Universidad de La Rioja (UR)
Repositorio:RIUR. Repositorio Institucional de la Universidad de La Rioja
OAI Identifier:oai:portal.dialnet.es:doc/5bbc67f2b750603269e800c4
Acceso en línea:https://investigacion.unirioja.es/documentos/5bbc67f2b750603269e800c4
Access Level:acceso abierto
Palabra clave:box-counting
Chebyshev-Halley methods
fractal dimension
Julia set
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spelling Fractal dimension of the universal Julia sets for the Chebyshev-Halley family of methodsGutiérrez, J.M. [0000-0002-0434-7250]Magreñán, Á.A. [0000-0002-6991-5706]Varona, J.L. [0000-0002-2023-9946]box-countingChebyshev-Halley methodsfractal dimensionJulia setThe concept of universal Julia set introduced in [5] allows us to conclude that the dynamics of a root-finding algorithm applied to any quadratic polynomial can be understood through the analysis of a particular rational map. In this study we go a step beyond in this direction. In particular, we can define the universal fractal dimension of the aforementioned algorithms as the fractal dimension of they corresponding universal Julia sets. © 2011 American Institute of Physics.2011info:eu-repo/semantics/bookPartinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://investigacion.unirioja.es/documentos/5bbc67f2b750603269e800c4reponame:RIUR. Repositorio Institucional de la Universidad de La Riojainstname:Universidad de La Rioja (UR)Inglésinfo:eu-repo/semantics/altIdentifier/doi/10.1063/1.3637794info:eu-repo/semantics/altIdentifier/wos/WOS:000302239800259info:eu-repo/semantics/altIdentifier/isbn/978-073540956-9Fractal dimension of the universal Julia sets for the Chebyshev-Halley family of methods, 2011, vol. 1389, pág. 1061-1064info:eu-repo/semantics/openAccessoai:portal.dialnet.es:doc/5bbc67f2b750603269e800c42026-06-14T12:47:17Z
dc.title.none.fl_str_mv Fractal dimension of the universal Julia sets for the Chebyshev-Halley family of methods
title Fractal dimension of the universal Julia sets for the Chebyshev-Halley family of methods
spellingShingle Fractal dimension of the universal Julia sets for the Chebyshev-Halley family of methods
Gutiérrez, J.M. [0000-0002-0434-7250]
box-counting
Chebyshev-Halley methods
fractal dimension
Julia set
title_short Fractal dimension of the universal Julia sets for the Chebyshev-Halley family of methods
title_full Fractal dimension of the universal Julia sets for the Chebyshev-Halley family of methods
title_fullStr Fractal dimension of the universal Julia sets for the Chebyshev-Halley family of methods
title_full_unstemmed Fractal dimension of the universal Julia sets for the Chebyshev-Halley family of methods
title_sort Fractal dimension of the universal Julia sets for the Chebyshev-Halley family of methods
dc.creator.none.fl_str_mv Gutiérrez, J.M. [0000-0002-0434-7250]
Magreñán, Á.A. [0000-0002-6991-5706]
Varona, J.L. [0000-0002-2023-9946]
author Gutiérrez, J.M. [0000-0002-0434-7250]
author_facet Gutiérrez, J.M. [0000-0002-0434-7250]
Magreñán, Á.A. [0000-0002-6991-5706]
Varona, J.L. [0000-0002-2023-9946]
author_role author
author2 Magreñán, Á.A. [0000-0002-6991-5706]
Varona, J.L. [0000-0002-2023-9946]
author2_role author
author
dc.subject.none.fl_str_mv box-counting
Chebyshev-Halley methods
fractal dimension
Julia set
topic box-counting
Chebyshev-Halley methods
fractal dimension
Julia set
description The concept of universal Julia set introduced in [5] allows us to conclude that the dynamics of a root-finding algorithm applied to any quadratic polynomial can be understood through the analysis of a particular rational map. In this study we go a step beyond in this direction. In particular, we can define the universal fractal dimension of the aforementioned algorithms as the fractal dimension of they corresponding universal Julia sets. © 2011 American Institute of Physics.
publishDate 2011
dc.date.none.fl_str_mv 2011
dc.type.none.fl_str_mv info:eu-repo/semantics/bookPart
info:eu-repo/semantics/acceptedVersion
format bookPart
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://investigacion.unirioja.es/documentos/5bbc67f2b750603269e800c4
url https://investigacion.unirioja.es/documentos/5bbc67f2b750603269e800c4
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1063/1.3637794
info:eu-repo/semantics/altIdentifier/wos/WOS:000302239800259
info:eu-repo/semantics/altIdentifier/isbn/978-073540956-9
Fractal dimension of the universal Julia sets for the Chebyshev-Halley family of methods, 2011, vol. 1389, pág. 1061-1064
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:RIUR. Repositorio Institucional de la Universidad de La Rioja
instname:Universidad de La Rioja (UR)
instname_str Universidad de La Rioja (UR)
reponame_str RIUR. Repositorio Institucional de la Universidad de La Rioja
collection RIUR. Repositorio Institucional de la Universidad de La Rioja
repository.name.fl_str_mv
repository.mail.fl_str_mv
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