On periodic and chaotic regions in the Mandelbrot set

11 pages, 5 figures.-- Available online Dec 20, 2005.

Bibliographic Details
Authors: Pastor, Gerardo, Romera, Miguel, Álvarez Marañón, Gonzalo, Arroyo Guardeño, David, Montoya Vitini, Fausto
Format: article
Publication Date:2007
Country:España
Institution:Consejo Superior de Investigaciones Científicas (CSIC)
Repository:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/2675
Online Access:http://hdl.handle.net/10261/2675
Access Level:Open access
Keyword:Mandelbrot set
Chaotic regions
Periodic regions
Nonlinear science
Chaos
id ES_5cc98df11694fdbce45f3553aa6ff0e7
oai_identifier_str oai:digital.csic.es:10261/2675
network_acronym_str ES
network_name_str España
repository_id_str
spelling On periodic and chaotic regions in the Mandelbrot setPastor, GerardoRomera, MiguelÁlvarez Marañón, GonzaloArroyo Guardeño, DavidMontoya Vitini, FaustoMandelbrot setChaotic regionsPeriodic regionsNonlinear scienceChaos11 pages, 5 figures.-- Available online Dec 20, 2005.We show here in a graphic and simple way the relation between the periodic and chaotic regions in the Mandelbrot set. Since the relation between the periodic and chaotic regions in a one-dimensional (1D) quadratic set is already well known, we shall base on it to extend the results to the Mandelbrot set. We shall see that in the same way as the hyperbolic components of the period-doubling cascade determines the chaotic bands structure in 1D quadratic sets, the periodic region determines the chaotic region in the Mandelbrot set.This work was supported by "Ministerio de Educación y Ciencia" of Spain, research grant SEG2004-02418.Peer reviewedElsevier200820082007info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_650122195 bytesapplication/pdfhttp://hdl.handle.net/10261/2675reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Ingléshttp://dx.doi.org/10.1016/j.chaos.2005.10.099info:eu-repo/semantics/openAccessoai:digital.csic.es:10261/26752026-05-22T06:33:51Z
dc.title.none.fl_str_mv On periodic and chaotic regions in the Mandelbrot set
title On periodic and chaotic regions in the Mandelbrot set
spellingShingle On periodic and chaotic regions in the Mandelbrot set
Pastor, Gerardo
Mandelbrot set
Chaotic regions
Periodic regions
Nonlinear science
Chaos
title_short On periodic and chaotic regions in the Mandelbrot set
title_full On periodic and chaotic regions in the Mandelbrot set
title_fullStr On periodic and chaotic regions in the Mandelbrot set
title_full_unstemmed On periodic and chaotic regions in the Mandelbrot set
title_sort On periodic and chaotic regions in the Mandelbrot set
dc.creator.none.fl_str_mv Pastor, Gerardo
Romera, Miguel
Álvarez Marañón, Gonzalo
Arroyo Guardeño, David
Montoya Vitini, Fausto
author Pastor, Gerardo
author_facet Pastor, Gerardo
Romera, Miguel
Álvarez Marañón, Gonzalo
Arroyo Guardeño, David
Montoya Vitini, Fausto
author_role author
author2 Romera, Miguel
Álvarez Marañón, Gonzalo
Arroyo Guardeño, David
Montoya Vitini, Fausto
author2_role author
author
author
author
dc.subject.none.fl_str_mv Mandelbrot set
Chaotic regions
Periodic regions
Nonlinear science
Chaos
topic Mandelbrot set
Chaotic regions
Periodic regions
Nonlinear science
Chaos
description 11 pages, 5 figures.-- Available online Dec 20, 2005.
publishDate 2007
dc.date.none.fl_str_mv 2007
2008
2008
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/2675
url http://hdl.handle.net/10261/2675
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv http://dx.doi.org/10.1016/j.chaos.2005.10.099
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 22195 bytes
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869408952553308160
score 15,811543

Similar Items