Dynamics of the coquaternionic maps x^2 + bx

Bibliographic Details
Main Author: Falcão, M. I.
Publication Date: 2023
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/1822/83464
Summary: This paper deals with the dynamics of the one-parameter family of coquaternionic quadratic maps x2+ bx. By making use of recent results for the zeros of one-sided coquaternionic polynomials, the fixed points are analytically determined. The stability of these fixed points is also addressed, where, in some cases, due to the appearance of sets of non-isolated points, a suitably adapted notion of stability is used. The results obtained show clearly that this family is not dynamically equivalent to the simpler family x2+ c previously studied by the authors. Some numerical examples of other dynamics beyond fixed points are also presented.
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spelling Dynamics of the coquaternionic maps x^2 + bxCoquaternionic polynomialsCoquaternionsFixed pointsIteration of quadratic mapsCiências Naturais::MatemáticasScience & TechnologyThis paper deals with the dynamics of the one-parameter family of coquaternionic quadratic maps x2+ bx. By making use of recent results for the zeros of one-sided coquaternionic polynomials, the fixed points are analytically determined. The stability of these fixed points is also addressed, where, in some cases, due to the appearance of sets of non-isolated points, a suitably adapted notion of stability is used. The results obtained show clearly that this family is not dynamically equivalent to the simpler family x2+ c previously studied by the authors. Some numerical examples of other dynamics beyond fixed points are also presented.Research at CMAT was partially financed by Portuguese funds through FCT - Fundação para a Ciência e a Tecnologia, within the Projects UIDB/00013/2020 and UIDP/00013/2020. Research at NIPE has been financed by National Funds of the FCT - Fundação para a Ciência e a Tecnologia, within the Project UIDB/03182/2020.SpringerUniversidade do MinhoFalcão, M. I.Miranda, FernandoSeverino, RicardoSoares, M. J.20232023-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/83464engFalcão, M. I., Miranda, F., Severino, R., & Soares, M. J. (2022, January 25). Dynamics of the coquaternionic maps x2 + bx. Rendiconti del Circolo Matematico di Palermo Series 2. Springer Science and Business Media LLC. http://doi.org/10.1007/s12215-021-00715-60009-725X1973-440910.1007/s12215-021-00715-6https://doi.org/10.1007/s12215-021-00715-6info: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:RCAAP2024-06-08T01:19:09Zoai:repositorium.sdum.uminho.pt:1822/83464Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T14:40:46.069006Repositórios 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 Dynamics of the coquaternionic maps x^2 + bx
title Dynamics of the coquaternionic maps x^2 + bx
spellingShingle Dynamics of the coquaternionic maps x^2 + bx
Falcão, M. I.
Coquaternionic polynomials
Coquaternions
Fixed points
Iteration of quadratic maps
Ciências Naturais::Matemáticas
Science & Technology
title_short Dynamics of the coquaternionic maps x^2 + bx
title_full Dynamics of the coquaternionic maps x^2 + bx
title_fullStr Dynamics of the coquaternionic maps x^2 + bx
title_full_unstemmed Dynamics of the coquaternionic maps x^2 + bx
title_sort Dynamics of the coquaternionic maps x^2 + bx
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 Coquaternionic polynomials
Coquaternions
Fixed points
Iteration of quadratic maps
Ciências Naturais::Matemáticas
Science & Technology
topic Coquaternionic polynomials
Coquaternions
Fixed points
Iteration of quadratic maps
Ciências Naturais::Matemáticas
Science & Technology
description This paper deals with the dynamics of the one-parameter family of coquaternionic quadratic maps x2+ bx. By making use of recent results for the zeros of one-sided coquaternionic polynomials, the fixed points are analytically determined. The stability of these fixed points is also addressed, where, in some cases, due to the appearance of sets of non-isolated points, a suitably adapted notion of stability is used. The results obtained show clearly that this family is not dynamically equivalent to the simpler family x2+ c previously studied by the authors. Some numerical examples of other dynamics beyond fixed points are also presented.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-01-01T00:00:00Z
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/1822/83464
url https://hdl.handle.net/1822/83464
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Falcão, M. I., Miranda, F., Severino, R., & Soares, M. J. (2022, January 25). Dynamics of the coquaternionic maps x2 + bx. Rendiconti del Circolo Matematico di Palermo Series 2. Springer Science and Business Media LLC. http://doi.org/10.1007/s12215-021-00715-6
0009-725X
1973-4409
10.1007/s12215-021-00715-6
https://doi.org/10.1007/s12215-021-00715-6
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 Springer
publisher.none.fl_str_mv Springer
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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