Uniqueness of Limit Cycle For Liénard differential Equations of Degree Four

We prove that any classical Liénard differential equation of degree four has at most one limit cycle, and the limit cycle is hyperbolic if it exists. This result gives a positive answer to the conjecture by A. Lins, W. de Melo and C. C. Pugh [4] in 1977 about the number of limit cycles for polynomia...

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Detalles Bibliográficos
Autores: Li, Chengzhi, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150546
Acceso en línea:https://ddd.uab.cat/record/150546
https://dx.doi.org/urn:doi:10.1016/j.jde.2011.11.002
Access Level:acceso abierto
Palabra clave:Liénard equations
Limit cycle
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spelling Uniqueness of Limit Cycle For Liénard differential Equations of Degree FourLi, ChengzhiLlibre, Jaume|||0000-0002-9511-5999Liénard equationsLimit cycleWe prove that any classical Liénard differential equation of degree four has at most one limit cycle, and the limit cycle is hyperbolic if it exists. This result gives a positive answer to the conjecture by A. Lins, W. de Melo and C. C. Pugh [4] in 1977 about the number of limit cycles for polynomial Liénard differential equations for n = 4. 22012-01-0120122012-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/150546https://dx.doi.org/urn:doi:10.1016/j.jde.2011.11.002reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-03437Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2009/SGR-410open accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:1505462026-06-06T12:50:31Z
dc.title.none.fl_str_mv Uniqueness of Limit Cycle For Liénard differential Equations of Degree Four
title Uniqueness of Limit Cycle For Liénard differential Equations of Degree Four
spellingShingle Uniqueness of Limit Cycle For Liénard differential Equations of Degree Four
Li, Chengzhi
Liénard equations
Limit cycle
title_short Uniqueness of Limit Cycle For Liénard differential Equations of Degree Four
title_full Uniqueness of Limit Cycle For Liénard differential Equations of Degree Four
title_fullStr Uniqueness of Limit Cycle For Liénard differential Equations of Degree Four
title_full_unstemmed Uniqueness of Limit Cycle For Liénard differential Equations of Degree Four
title_sort Uniqueness of Limit Cycle For Liénard differential Equations of Degree Four
dc.creator.none.fl_str_mv Li, Chengzhi
Llibre, Jaume|||0000-0002-9511-5999
author Li, Chengzhi
author_facet Li, Chengzhi
Llibre, Jaume|||0000-0002-9511-5999
author_role author
author2 Llibre, Jaume|||0000-0002-9511-5999
author2_role author
dc.subject.none.fl_str_mv Liénard equations
Limit cycle
topic Liénard equations
Limit cycle
description We prove that any classical Liénard differential equation of degree four has at most one limit cycle, and the limit cycle is hyperbolic if it exists. This result gives a positive answer to the conjecture by A. Lins, W. de Melo and C. C. Pugh [4] in 1977 about the number of limit cycles for polynomial Liénard differential equations for n = 4.
publishDate 2012
dc.date.none.fl_str_mv 2
2012-01-01
2012
2012-01-01
dc.type.none.fl_str_mv Article
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dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
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https://dx.doi.org/urn:doi:10.1016/j.jde.2011.11.002
url https://ddd.uab.cat/record/150546
https://dx.doi.org/urn:doi:10.1016/j.jde.2011.11.002
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2008-03437
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2009/SGR-410
dc.rights.none.fl_str_mv open access
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instname:Universitat Autònoma de Barcelona
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