Iteration of quadratic maps on matrix algebras

Bibliographic Details
Main Author: Baptista, Alexandra Nascimento
Publication Date: 2012
Other Authors: Ramos, Carlos Correia, Martins, Nuno
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10174/7862
https://doi.org/10.1142/S0218127412501507
Summary: We study the iteration of a quadratic family in the algebra of 2 × 2 real matrices, parameterized by a matrix C. We analyze and classify the existing cycles (periodic orbits) and their dependence on the parameter matrix. We discuss how new dynamical phenomena occur as a consequence of the noncommutativity of the matrix product. In particular, we show that the commutator of the initial condition with parameter matrix C has a decisive role in the overall dynamics.
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spelling Iteration of quadratic maps on matrix algebrasMatrix dynamicsiterated interval mapsnoncommuting attractive cyclesWe study the iteration of a quadratic family in the algebra of 2 × 2 real matrices, parameterized by a matrix C. We analyze and classify the existing cycles (periodic orbits) and their dependence on the parameter matrix. We discuss how new dynamical phenomena occur as a consequence of the noncommutativity of the matrix product. In particular, we show that the commutator of the initial condition with parameter matrix C has a decisive role in the overall dynamics.World Scientific Publishing Co2013-01-29T11:15:32Z2013-01-292012-06-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10174/7862http://hdl.handle.net/10174/7862https://doi.org/10.1142/S0218127412501507engNascimento Baptista, Alexandra; Correia Ramos, Carlos; Martins, Nuno Iteration of quadratic maps on matrix algebras. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 22 (2012), no. 6, 1250150, 7 pp.DMATalexandra.nascimento@ipleiria.ptccr@uevora.ptnmartins@math.ist.utl.pt721Baptista, Alexandra NascimentoRamos, Carlos CorreiaMartins, Nunoinfo: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:RCAAP2024-01-03T18:48:35Zoai:dspace.uevora.pt:10174/7862Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T11:58:05.959320Repositórios 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 Iteration of quadratic maps on matrix algebras
title Iteration of quadratic maps on matrix algebras
spellingShingle Iteration of quadratic maps on matrix algebras
Baptista, Alexandra Nascimento
Matrix dynamics
iterated interval maps
noncommuting attractive cycles
title_short Iteration of quadratic maps on matrix algebras
title_full Iteration of quadratic maps on matrix algebras
title_fullStr Iteration of quadratic maps on matrix algebras
title_full_unstemmed Iteration of quadratic maps on matrix algebras
title_sort Iteration of quadratic maps on matrix algebras
author Baptista, Alexandra Nascimento
author_facet Baptista, Alexandra Nascimento
Ramos, Carlos Correia
Martins, Nuno
author_role author
author2 Ramos, Carlos Correia
Martins, Nuno
author2_role author
author
dc.contributor.author.fl_str_mv Baptista, Alexandra Nascimento
Ramos, Carlos Correia
Martins, Nuno
dc.subject.por.fl_str_mv Matrix dynamics
iterated interval maps
noncommuting attractive cycles
topic Matrix dynamics
iterated interval maps
noncommuting attractive cycles
description We study the iteration of a quadratic family in the algebra of 2 × 2 real matrices, parameterized by a matrix C. We analyze and classify the existing cycles (periodic orbits) and their dependence on the parameter matrix. We discuss how new dynamical phenomena occur as a consequence of the noncommutativity of the matrix product. In particular, we show that the commutator of the initial condition with parameter matrix C has a decisive role in the overall dynamics.
publishDate 2012
dc.date.none.fl_str_mv 2012-06-01T00:00:00Z
2013-01-29T11:15:32Z
2013-01-29
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 http://hdl.handle.net/10174/7862
http://hdl.handle.net/10174/7862
https://doi.org/10.1142/S0218127412501507
url http://hdl.handle.net/10174/7862
https://doi.org/10.1142/S0218127412501507
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Nascimento Baptista, Alexandra; Correia Ramos, Carlos; Martins, Nuno Iteration of quadratic maps on matrix algebras. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 22 (2012), no. 6, 1250150, 7 pp.
DMAT
alexandra.nascimento@ipleiria.pt
ccr@uevora.pt
nmartins@math.ist.utl.pt
721
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv World Scientific Publishing Co
publisher.none.fl_str_mv World Scientific Publishing Co
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
_version_ 1833592385127317504

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