Global phase portraits of Kukles differential systems with homogenous polynomial nonlinearities of degree 5 having a center and their small limit cycles

We provide the nine topological global phase portraits in the Poincaré disk of the family of the centers of Kukles polynomial differential systems of the form x = -y, y= x ax^5y bx^3y^3 cxy^5, where x,y\R and a,b,c are real parameters satisfying a^2 b^2 c^2 0. Using averaging theory up to sixth orde...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Silva, Mauricio Fronza da
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:169460
Acceso en línea:https://ddd.uab.cat/record/169460
https://dx.doi.org/urn:doi:10.1142/S0218127416500449
Access Level:acceso abierto
Palabra clave:Centers
Kukles
Phase portrait
Poincaré disk
Polynomial vector fields
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spelling Global phase portraits of Kukles differential systems with homogenous polynomial nonlinearities of degree 5 having a center and their small limit cyclesLlibre, Jaume|||0000-0002-9511-5999Silva, Mauricio Fronza daCentersKuklesPhase portraitPoincaré diskPolynomial vector fieldsWe provide the nine topological global phase portraits in the Poincaré disk of the family of the centers of Kukles polynomial differential systems of the form x = -y, y= x ax^5y bx^3y^3 cxy^5, where x,y\R and a,b,c are real parameters satisfying a^2 b^2 c^2 0. Using averaging theory up to sixth order we determine the number of limit cycles which bifurcate from the origin when we perturb this system first inside the class of all homogeneous polynomial differential systems of degree 6, and second inside the class of all polynomial differential systems of degree 6. 22016-01-0120162016-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/169460https://dx.doi.org/urn:doi:10.1142/S0218127416500449reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengopen 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:1694602026-06-06T12:50:31Z
dc.title.none.fl_str_mv Global phase portraits of Kukles differential systems with homogenous polynomial nonlinearities of degree 5 having a center and their small limit cycles
title Global phase portraits of Kukles differential systems with homogenous polynomial nonlinearities of degree 5 having a center and their small limit cycles
spellingShingle Global phase portraits of Kukles differential systems with homogenous polynomial nonlinearities of degree 5 having a center and their small limit cycles
Llibre, Jaume|||0000-0002-9511-5999
Centers
Kukles
Phase portrait
Poincaré disk
Polynomial vector fields
title_short Global phase portraits of Kukles differential systems with homogenous polynomial nonlinearities of degree 5 having a center and their small limit cycles
title_full Global phase portraits of Kukles differential systems with homogenous polynomial nonlinearities of degree 5 having a center and their small limit cycles
title_fullStr Global phase portraits of Kukles differential systems with homogenous polynomial nonlinearities of degree 5 having a center and their small limit cycles
title_full_unstemmed Global phase portraits of Kukles differential systems with homogenous polynomial nonlinearities of degree 5 having a center and their small limit cycles
title_sort Global phase portraits of Kukles differential systems with homogenous polynomial nonlinearities of degree 5 having a center and their small limit cycles
dc.creator.none.fl_str_mv Llibre, Jaume|||0000-0002-9511-5999
Silva, Mauricio Fronza da
author Llibre, Jaume|||0000-0002-9511-5999
author_facet Llibre, Jaume|||0000-0002-9511-5999
Silva, Mauricio Fronza da
author_role author
author2 Silva, Mauricio Fronza da
author2_role author
dc.subject.none.fl_str_mv Centers
Kukles
Phase portrait
Poincaré disk
Polynomial vector fields
topic Centers
Kukles
Phase portrait
Poincaré disk
Polynomial vector fields
description We provide the nine topological global phase portraits in the Poincaré disk of the family of the centers of Kukles polynomial differential systems of the form x = -y, y= x ax^5y bx^3y^3 cxy^5, where x,y\R and a,b,c are real parameters satisfying a^2 b^2 c^2 0. Using averaging theory up to sixth order we determine the number of limit cycles which bifurcate from the origin when we perturb this system first inside the class of all homogeneous polynomial differential systems of degree 6, and second inside the class of all polynomial differential systems of degree 6.
publishDate 2016
dc.date.none.fl_str_mv 2
2016-01-01
2016
2016-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/169460
https://dx.doi.org/urn:doi:10.1142/S0218127416500449
url https://ddd.uab.cat/record/169460
https://dx.doi.org/urn:doi:10.1142/S0218127416500449
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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