On the limit cycles of linear differential systems with homogeneous nonlinearities

We consider the class of polynomial differential systems of the form x'= x - y P_n (x, y), y'=x y Q_n (x, y), where P_n and Q_n are homogeneous polynomials of degree n. For this class of differential systems we summarize the known results for the existence of limit cycles, and we provide n...

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Authors: Llibre, Jaume|||0000-0002-9511-5999, Zhang, Xiang
Format: article
Publication Date:2015
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:145301
Online Access:https://ddd.uab.cat/record/145301
https://dx.doi.org/urn:doi:10.4153/CMB-2015-062-1
Access Level:Open access
Keyword:Differential equations on the cylinder
Limit cycles
Polynomial differential system
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spelling On the limit cycles of linear differential systems with homogeneous nonlinearitiesLlibre, Jaume|||0000-0002-9511-5999Zhang, XiangDifferential equations on the cylinderLimit cyclesPolynomial differential systemWe consider the class of polynomial differential systems of the form x'= x - y P_n (x, y), y'=x y Q_n (x, y), where P_n and Q_n are homogeneous polynomials of degree n. For this class of differential systems we summarize the known results for the existence of limit cycles, and we provide new results for their nonexistence and existence. 22015-01-0120152015-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/145301https://dx.doi.org/urn:doi:10.4153/CMB-2015-062-1reponame: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 2014/SGR-410European Commission https://doi.org/10.13039/501100000780 316338European Commission https://doi.org/10.13039/501100000780 318999open 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:1453012026-06-06T12:50:31Z
dc.title.none.fl_str_mv On the limit cycles of linear differential systems with homogeneous nonlinearities
title On the limit cycles of linear differential systems with homogeneous nonlinearities
spellingShingle On the limit cycles of linear differential systems with homogeneous nonlinearities
Llibre, Jaume|||0000-0002-9511-5999
Differential equations on the cylinder
Limit cycles
Polynomial differential system
title_short On the limit cycles of linear differential systems with homogeneous nonlinearities
title_full On the limit cycles of linear differential systems with homogeneous nonlinearities
title_fullStr On the limit cycles of linear differential systems with homogeneous nonlinearities
title_full_unstemmed On the limit cycles of linear differential systems with homogeneous nonlinearities
title_sort On the limit cycles of linear differential systems with homogeneous nonlinearities
dc.creator.none.fl_str_mv Llibre, Jaume|||0000-0002-9511-5999
Zhang, Xiang
author Llibre, Jaume|||0000-0002-9511-5999
author_facet Llibre, Jaume|||0000-0002-9511-5999
Zhang, Xiang
author_role author
author2 Zhang, Xiang
author2_role author
dc.subject.none.fl_str_mv Differential equations on the cylinder
Limit cycles
Polynomial differential system
topic Differential equations on the cylinder
Limit cycles
Polynomial differential system
description We consider the class of polynomial differential systems of the form x'= x - y P_n (x, y), y'=x y Q_n (x, y), where P_n and Q_n are homogeneous polynomials of degree n. For this class of differential systems we summarize the known results for the existence of limit cycles, and we provide new results for their nonexistence and existence.
publishDate 2015
dc.date.none.fl_str_mv 2
2015-01-01
2015
2015-01-01
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/145301
https://dx.doi.org/urn:doi:10.4153/CMB-2015-062-1
url https://ddd.uab.cat/record/145301
https://dx.doi.org/urn:doi:10.4153/CMB-2015-062-1
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 2014/SGR-410
European Commission https://doi.org/10.13039/501100000780 316338
European Commission https://doi.org/10.13039/501100000780 318999
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
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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
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