Periodic perturbations of quadratic planar polynomial vector fields
Autor(a) principal: | |
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Data de Publicação: | 2002 |
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=S0001-37652002000200001 |
Resumo: | In this work are studied periodic perturbations, depending on two parameters, of quadratic planar polynomial vector fields having an infinite heteroclinic cycle, which is an unbounded solution joining two saddle points at infinity. The global study envolving infinity is performed via the Poincaré compactification. The main result obtained states that for certain types of periodic perturbations, the perturbed system has quadratic heteroclinic tangencies and transverse intersections between the local stable and unstable manifolds of the hyperbolic periodic orbits at infinity. It implies, via the Birkhoff-Smale Theorem, in a complex dynamical behavior of the solutions of the perturbed system, in a finite part of the phase plane. |
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Anais da Academia Brasileira de Ciências (Online) |
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Periodic perturbations of quadratic planar polynomial vector fieldsheteroclinic cyclesperiodic perturbationspolynomial systemsIn this work are studied periodic perturbations, depending on two parameters, of quadratic planar polynomial vector fields having an infinite heteroclinic cycle, which is an unbounded solution joining two saddle points at infinity. The global study envolving infinity is performed via the Poincaré compactification. The main result obtained states that for certain types of periodic perturbations, the perturbed system has quadratic heteroclinic tangencies and transverse intersections between the local stable and unstable manifolds of the hyperbolic periodic orbits at infinity. It implies, via the Birkhoff-Smale Theorem, in a complex dynamical behavior of the solutions of the perturbed system, in a finite part of the phase plane.Academia Brasileira de Ciências2002-06-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652002000200001Anais da Academia Brasileira de Ciências v.74 n.2 2002reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652002000200001info:eu-repo/semantics/openAccessMESSIAS,MARCELOeng2002-07-17T00:00:00Zoai:scielo:S0001-37652002000200001Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2002-07-17T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false |
dc.title.none.fl_str_mv |
Periodic perturbations of quadratic planar polynomial vector fields |
title |
Periodic perturbations of quadratic planar polynomial vector fields |
spellingShingle |
Periodic perturbations of quadratic planar polynomial vector fields MESSIAS,MARCELO heteroclinic cycles periodic perturbations polynomial systems |
title_short |
Periodic perturbations of quadratic planar polynomial vector fields |
title_full |
Periodic perturbations of quadratic planar polynomial vector fields |
title_fullStr |
Periodic perturbations of quadratic planar polynomial vector fields |
title_full_unstemmed |
Periodic perturbations of quadratic planar polynomial vector fields |
title_sort |
Periodic perturbations of quadratic planar polynomial vector fields |
author |
MESSIAS,MARCELO |
author_facet |
MESSIAS,MARCELO |
author_role |
author |
dc.contributor.author.fl_str_mv |
MESSIAS,MARCELO |
dc.subject.por.fl_str_mv |
heteroclinic cycles periodic perturbations polynomial systems |
topic |
heteroclinic cycles periodic perturbations polynomial systems |
description |
In this work are studied periodic perturbations, depending on two parameters, of quadratic planar polynomial vector fields having an infinite heteroclinic cycle, which is an unbounded solution joining two saddle points at infinity. The global study envolving infinity is performed via the Poincaré compactification. The main result obtained states that for certain types of periodic perturbations, the perturbed system has quadratic heteroclinic tangencies and transverse intersections between the local stable and unstable manifolds of the hyperbolic periodic orbits at infinity. It implies, via the Birkhoff-Smale Theorem, in a complex dynamical behavior of the solutions of the perturbed system, in a finite part of the phase plane. |
publishDate |
2002 |
dc.date.none.fl_str_mv |
2002-06-01 |
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=S0001-37652002000200001 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652002000200001 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S0001-37652002000200001 |
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.74 n.2 2002 reponame:Anais da Academia Brasileira de Ciências (Online) instname:Academia Brasileira de Ciências (ABC) instacron:ABC |
instname_str |
Academia Brasileira de Ciências (ABC) |
instacron_str |
ABC |
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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1754302855755333632 |