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Basins of attraction for a quadratic coquaternionic map

Bibliographic Details
Main Author: Falcão, M. I.
Publication Date: 2017
Other Authors: Miranda, Fernando, Severino, Ricardo, Soares, M. J.
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: https://hdl.handle.net/1822/48044
Summary: In this paper we consider the extension, to the algebra of coquaternions, of a complex quadratic map with a real super-attractive 8-cycle. We establish that, in addition to the real cycle, this new map has sets of non-isolated periodic points of period 8, forming four attractive 8-cycles. Here , the cycles are to be interpreted as cycles of sets and an appropriate notion of attractivity is used. Some characteristics of the basins of attraction of the five attracting 8-cycles are discussed and plots revealing the intertwined nature of these basins are shown.
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spelling Basins of attraction for a quadratic coquaternionic mapAttracting cyclesBasins of attractionCoquaternionsIteration of mapsScience & TechnologyIn this paper we consider the extension, to the algebra of coquaternions, of a complex quadratic map with a real super-attractive 8-cycle. We establish that, in addition to the real cycle, this new map has sets of non-isolated periodic points of period 8, forming four attractive 8-cycles. Here , the cycles are to be interpreted as cycles of sets and an appropriate notion of attractivity is used. Some characteristics of the basins of attraction of the five attracting 8-cycles are discussed and plots revealing the intertwined nature of these basins are shown.Research at CMAT was financed by Portuguese Funds through FCT - Funda¸c˜ao para a Ciˆencia e a Tecnologia, within the Project UID/MAT/00013/2013. Research at NIPE has been carried out within the funding with COMPETE reference number POCI-01- 0145-FEDER-006683, with the FCT/MEC’s (Funda¸c˜ao para a Ciˆencia e a Tecnologia, I.P.) financial support through national funding and by the ERDF through the Operational Programme on “Competitiveness and Internationalization – COMPETE 2020” under the PT2020 Partnership Agreement.info:eu-repo/semantics/publishedVersionElsevierUniversidade do MinhoFalcão, M. I.Miranda, FernandoSeverino, RicardoSoares, M. J.20172017-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/48044eng0960-077910.1016/j.chaos.2017.09.016info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-04-12T04:39:33Zoai:repositorium.sdum.uminho.pt:1822/48044Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T15:35:10.718015Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Basins of attraction for a quadratic coquaternionic map
title Basins of attraction for a quadratic coquaternionic map
spellingShingle Basins of attraction for a quadratic coquaternionic map
Falcão, M. I.
Attracting cycles
Basins of attraction
Coquaternions
Iteration of maps
Science & Technology
title_short Basins of attraction for a quadratic coquaternionic map
title_full Basins of attraction for a quadratic coquaternionic map
title_fullStr Basins of attraction for a quadratic coquaternionic map
title_full_unstemmed Basins of attraction for a quadratic coquaternionic map
title_sort Basins of attraction for a quadratic coquaternionic map
author Falcão, M. I.
author_facet Falcão, M. I.
Miranda, Fernando
Severino, Ricardo
Soares, M. J.
author_role author
author2 Miranda, Fernando
Severino, Ricardo
Soares, M. J.
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Falcão, M. I.
Miranda, Fernando
Severino, Ricardo
Soares, M. J.
dc.subject.por.fl_str_mv Attracting cycles
Basins of attraction
Coquaternions
Iteration of maps
Science & Technology
topic Attracting cycles
Basins of attraction
Coquaternions
Iteration of maps
Science & Technology
description In this paper we consider the extension, to the algebra of coquaternions, of a complex quadratic map with a real super-attractive 8-cycle. We establish that, in addition to the real cycle, this new map has sets of non-isolated periodic points of period 8, forming four attractive 8-cycles. Here , the cycles are to be interpreted as cycles of sets and an appropriate notion of attractivity is used. Some characteristics of the basins of attraction of the five attracting 8-cycles are discussed and plots revealing the intertwined nature of these basins are shown.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-01-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://hdl.handle.net/1822/48044
url https://hdl.handle.net/1822/48044
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0960-0779
10.1016/j.chaos.2017.09.016
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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