On the existence of infinite heteroclinic cycles in polynomial systems and its dynamic consequences
Autor(a) principal: | |
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Data de Publicação: | 2004 |
Outros Autores: | |
Tipo de documento: | Artigo de conferência |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://hdl.handle.net/11449/39610 |
Resumo: | In this work we consider the dynamic consequences of the existence of infinite heteroclinic cycle in planar polynomial vector fields, which is a trajectory connecting two saddle points at infinity. It is stated that, although the saddles which form the cycle belong to infinity, for certain types of nonautonomous perturbations the perturbed system may present a complex dynamic behavior of the solutions in a finite part of the phase plane, due to the existence of tangencies and transversal intersections of their stable and unstable manifolds. This phenomenon might be called the chaos arising from infinity. The global study at infinity is made via the Poincare Compactification and the argument used to prove the statement is the Birkhoff-Smale Theorem. (c) 2004 WILEY-NCH Verlag GmbH & Co. KGaA, Weinheim. |
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Repositório Institucional da UNESP |
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On the existence of infinite heteroclinic cycles in polynomial systems and its dynamic consequencesIn this work we consider the dynamic consequences of the existence of infinite heteroclinic cycle in planar polynomial vector fields, which is a trajectory connecting two saddle points at infinity. It is stated that, although the saddles which form the cycle belong to infinity, for certain types of nonautonomous perturbations the perturbed system may present a complex dynamic behavior of the solutions in a finite part of the phase plane, due to the existence of tangencies and transversal intersections of their stable and unstable manifolds. This phenomenon might be called the chaos arising from infinity. The global study at infinity is made via the Poincare Compactification and the argument used to prove the statement is the Birkhoff-Smale Theorem. (c) 2004 WILEY-NCH Verlag GmbH & Co. KGaA, Weinheim.UNESP, Dept Matemat Estatist & Comp, Fac Ciências & Tecnol, BR-19060900 São Paulo, BrazilUNESP, Dept Matemat Estatist & Comp, Fac Ciências & Tecnol, BR-19060900 São Paulo, BrazilWiley-BlackwellUniversidade Estadual Paulista (Unesp)Messias, Marcelo [UNESP]Meneguette Júnior, Messias [UNESP]2014-05-20T15:30:10Z2014-05-20T15:30:10Z2004-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObject261-264Icnaam 2004: International Conference on Numerical Analysis and Applied Mathematics 2004. Weinheim: Wiley-v C H Verlag Gmbh, p. 261-264, 2004.http://hdl.handle.net/11449/39610WOS:00022771750006837572256690563171531018187057108Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengIcnaam 2004: International Conference on Numerical Analysis and Applied Mathematics 2004info:eu-repo/semantics/openAccess2024-06-19T14:32:27Zoai:repositorio.unesp.br:11449/39610Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-06-19T14:32:27Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
On the existence of infinite heteroclinic cycles in polynomial systems and its dynamic consequences |
title |
On the existence of infinite heteroclinic cycles in polynomial systems and its dynamic consequences |
spellingShingle |
On the existence of infinite heteroclinic cycles in polynomial systems and its dynamic consequences Messias, Marcelo [UNESP] |
title_short |
On the existence of infinite heteroclinic cycles in polynomial systems and its dynamic consequences |
title_full |
On the existence of infinite heteroclinic cycles in polynomial systems and its dynamic consequences |
title_fullStr |
On the existence of infinite heteroclinic cycles in polynomial systems and its dynamic consequences |
title_full_unstemmed |
On the existence of infinite heteroclinic cycles in polynomial systems and its dynamic consequences |
title_sort |
On the existence of infinite heteroclinic cycles in polynomial systems and its dynamic consequences |
author |
Messias, Marcelo [UNESP] |
author_facet |
Messias, Marcelo [UNESP] Meneguette Júnior, Messias [UNESP] |
author_role |
author |
author2 |
Meneguette Júnior, Messias [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Messias, Marcelo [UNESP] Meneguette Júnior, Messias [UNESP] |
description |
In this work we consider the dynamic consequences of the existence of infinite heteroclinic cycle in planar polynomial vector fields, which is a trajectory connecting two saddle points at infinity. It is stated that, although the saddles which form the cycle belong to infinity, for certain types of nonautonomous perturbations the perturbed system may present a complex dynamic behavior of the solutions in a finite part of the phase plane, due to the existence of tangencies and transversal intersections of their stable and unstable manifolds. This phenomenon might be called the chaos arising from infinity. The global study at infinity is made via the Poincare Compactification and the argument used to prove the statement is the Birkhoff-Smale Theorem. (c) 2004 WILEY-NCH Verlag GmbH & Co. KGaA, Weinheim. |
publishDate |
2004 |
dc.date.none.fl_str_mv |
2004-01-01 2014-05-20T15:30:10Z 2014-05-20T15:30:10Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/conferenceObject |
format |
conferenceObject |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
Icnaam 2004: International Conference on Numerical Analysis and Applied Mathematics 2004. Weinheim: Wiley-v C H Verlag Gmbh, p. 261-264, 2004. http://hdl.handle.net/11449/39610 WOS:000227717500068 3757225669056317 1531018187057108 |
identifier_str_mv |
Icnaam 2004: International Conference on Numerical Analysis and Applied Mathematics 2004. Weinheim: Wiley-v C H Verlag Gmbh, p. 261-264, 2004. WOS:000227717500068 3757225669056317 1531018187057108 |
url |
http://hdl.handle.net/11449/39610 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Icnaam 2004: International Conference on Numerical Analysis and Applied Mathematics 2004 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
261-264 |
dc.publisher.none.fl_str_mv |
Wiley-Blackwell |
publisher.none.fl_str_mv |
Wiley-Blackwell |
dc.source.none.fl_str_mv |
Web of Science reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1803045463098654720 |