Large amplitude oscillations for a class of symmetric polynomial differential systems in R³

Detalhes bibliográficos
Autor(a) principal: Llibre,Jaume
Data de Publicação: 2007
Outros Autores: Messias,Marcelo
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Anais da Academia Brasileira de Ciências (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652007000400001
Resumo: In this paper we study a class of symmetric polynomial differential systems in R³, which has a set of parallel invariant straight lines, forming degenerate heteroclinic cycles, which have their two singular endpoints at infinity. The global study near infinity is performed using the Poincaré compactification. We prove that for all n <FONT FACE=Symbol>Î</FONT> N there is epsilonn > 0 such that for 0 < epsilon < epsilonn the system has at least n large amplitude periodic orbits bifurcating from the heteroclinic loop formed by the two invariant straight lines closest to the x-axis, one contained in the half-space y > 0 and the other in y < 0.
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spelling Large amplitude oscillations for a class of symmetric polynomial differential systems in R³infinite heteroclinic loopsperiodic orbitssymmetric systemsIn this paper we study a class of symmetric polynomial differential systems in R³, which has a set of parallel invariant straight lines, forming degenerate heteroclinic cycles, which have their two singular endpoints at infinity. The global study near infinity is performed using the Poincaré compactification. We prove that for all n <FONT FACE=Symbol>Î</FONT> N there is epsilonn > 0 such that for 0 < epsilon < epsilonn the system has at least n large amplitude periodic orbits bifurcating from the heteroclinic loop formed by the two invariant straight lines closest to the x-axis, one contained in the half-space y > 0 and the other in y < 0.Academia Brasileira de Ciências2007-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652007000400001Anais da Academia Brasileira de Ciências v.79 n.4 2007reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652007000400001info:eu-repo/semantics/openAccessLlibre,JaumeMessias,Marceloeng2008-04-11T00:00:00Zoai:scielo:S0001-37652007000400001Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2008-04-11T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv Large amplitude oscillations for a class of symmetric polynomial differential systems in R³
title Large amplitude oscillations for a class of symmetric polynomial differential systems in R³
spellingShingle Large amplitude oscillations for a class of symmetric polynomial differential systems in R³
Llibre,Jaume
infinite heteroclinic loops
periodic orbits
symmetric systems
title_short Large amplitude oscillations for a class of symmetric polynomial differential systems in R³
title_full Large amplitude oscillations for a class of symmetric polynomial differential systems in R³
title_fullStr Large amplitude oscillations for a class of symmetric polynomial differential systems in R³
title_full_unstemmed Large amplitude oscillations for a class of symmetric polynomial differential systems in R³
title_sort Large amplitude oscillations for a class of symmetric polynomial differential systems in R³
author Llibre,Jaume
author_facet Llibre,Jaume
Messias,Marcelo
author_role author
author2 Messias,Marcelo
author2_role author
dc.contributor.author.fl_str_mv Llibre,Jaume
Messias,Marcelo
dc.subject.por.fl_str_mv infinite heteroclinic loops
periodic orbits
symmetric systems
topic infinite heteroclinic loops
periodic orbits
symmetric systems
description In this paper we study a class of symmetric polynomial differential systems in R³, which has a set of parallel invariant straight lines, forming degenerate heteroclinic cycles, which have their two singular endpoints at infinity. The global study near infinity is performed using the Poincaré compactification. We prove that for all n <FONT FACE=Symbol>Î</FONT> N there is epsilonn > 0 such that for 0 < epsilon < epsilonn the system has at least n large amplitude periodic orbits bifurcating from the heteroclinic loop formed by the two invariant straight lines closest to the x-axis, one contained in the half-space y > 0 and the other in y < 0.
publishDate 2007
dc.date.none.fl_str_mv 2007-12-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652007000400001
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652007000400001
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0001-37652007000400001
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Academia Brasileira de Ciências
publisher.none.fl_str_mv Academia Brasileira de Ciências
dc.source.none.fl_str_mv Anais da Academia Brasileira de Ciências v.79 n.4 2007
reponame:Anais da Academia Brasileira de Ciências (Online)
instname:Academia Brasileira de Ciências (ABC)
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instname_str Academia Brasileira de Ciências (ABC)
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institution ABC
reponame_str Anais da Academia Brasileira de Ciências (Online)
collection Anais da Academia Brasileira de Ciências (Online)
repository.name.fl_str_mv Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)
repository.mail.fl_str_mv ||aabc@abc.org.br
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