Plenty of hyperbolicity on a class of linear homogeneous jerk differential equations

Detalhes bibliográficos
Autor(a) principal: Bessa, Mário
Data de Publicação: 2023
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.2/13928
Resumo: We consider 3×3 partially hyperbolic linear differential systems over an ergodic flow X^t and derived from the linear homogeneous differential equation x''(t)+β(X^t(t))x'(t)+ γ(t)x(t) = 0. Assuming that the partial hyperbolic decomposition E^s ⊕ E^c ⊕ E^u is proper and displays a zero Lyapunov exponent along the central direction E^c we prove that some C^0 perturbation of the parameters β(t) and γ(t) can be done in order to obtain non-zero Lyapunov exponents and so a chaotic behaviour of the solution.
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spelling Plenty of hyperbolicity on a class of linear homogeneous jerk differential equationsLyapunov exponentsJerk equationsPartial hyperbolicityWe consider 3×3 partially hyperbolic linear differential systems over an ergodic flow X^t and derived from the linear homogeneous differential equation x''(t)+β(X^t(t))x'(t)+ γ(t)x(t) = 0. Assuming that the partial hyperbolic decomposition E^s ⊕ E^c ⊕ E^u is proper and displays a zero Lyapunov exponent along the central direction E^c we prove that some C^0 perturbation of the parameters β(t) and γ(t) can be done in order to obtain non-zero Lyapunov exponents and so a chaotic behaviour of the solution.SpringerRepositório AbertoBessa, Mário2023-05-31T11:58:10Z20232023-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/13928engBessa, M. Plenty of hyperbolicity on a class of linear homogeneous jerk differential equations. Aequat. Math. 97, 467–487 (2023)0001-905410.1007/s00010-023-00948-zinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-16T15:46:07Zoai:repositorioaberto.uab.pt:10400.2/13928Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:52:45.746319Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Plenty of hyperbolicity on a class of linear homogeneous jerk differential equations
title Plenty of hyperbolicity on a class of linear homogeneous jerk differential equations
spellingShingle Plenty of hyperbolicity on a class of linear homogeneous jerk differential equations
Bessa, Mário
Lyapunov exponents
Jerk equations
Partial hyperbolicity
title_short Plenty of hyperbolicity on a class of linear homogeneous jerk differential equations
title_full Plenty of hyperbolicity on a class of linear homogeneous jerk differential equations
title_fullStr Plenty of hyperbolicity on a class of linear homogeneous jerk differential equations
title_full_unstemmed Plenty of hyperbolicity on a class of linear homogeneous jerk differential equations
title_sort Plenty of hyperbolicity on a class of linear homogeneous jerk differential equations
author Bessa, Mário
author_facet Bessa, Mário
author_role author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Bessa, Mário
dc.subject.por.fl_str_mv Lyapunov exponents
Jerk equations
Partial hyperbolicity
topic Lyapunov exponents
Jerk equations
Partial hyperbolicity
description We consider 3×3 partially hyperbolic linear differential systems over an ergodic flow X^t and derived from the linear homogeneous differential equation x''(t)+β(X^t(t))x'(t)+ γ(t)x(t) = 0. Assuming that the partial hyperbolic decomposition E^s ⊕ E^c ⊕ E^u is proper and displays a zero Lyapunov exponent along the central direction E^c we prove that some C^0 perturbation of the parameters β(t) and γ(t) can be done in order to obtain non-zero Lyapunov exponents and so a chaotic behaviour of the solution.
publishDate 2023
dc.date.none.fl_str_mv 2023-05-31T11:58:10Z
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 http://hdl.handle.net/10400.2/13928
url http://hdl.handle.net/10400.2/13928
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Bessa, M. Plenty of hyperbolicity on a class of linear homogeneous jerk differential equations. Aequat. Math. 97, 467–487 (2023)
0001-9054
10.1007/s00010-023-00948-z
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:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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