Highest weak focus order for trigonometric Liénard equations

Given a planar analytic differential equation with a critical point which is a weak focus of order k, it is well known that at most k limit cycles can bifurcate from it. Moreover, in case of analytic Liénard differential equations this order can be computed as one half of the multiplicity of an asso...

Descripción completa

Detalles Bibliográficos
Autores: Gasull, Armengol|||0000-0002-1719-8231, Giné, Jaume|||0000-0001-7109-2553, Valls, Clàudia|||0000-0001-8279-1229
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:221357
Acceso en línea:https://ddd.uab.cat/record/221357
https://dx.doi.org/urn:doi:10.1007/s10231-019-00936-8
Access Level:acceso abierto
Palabra clave:Trigonometric Liénard equation
Weak focus
Cyclicity
id ES_aecc5bbe71b534e2555e2a8d62aedd00
oai_identifier_str oai:ddd.uab.cat:221357
network_acronym_str ES
network_name_str España
repository_id_str
spelling Highest weak focus order for trigonometric Liénard equationsGasull, Armengol|||0000-0002-1719-8231Giné, Jaume|||0000-0001-7109-2553Valls, Clàudia|||0000-0001-8279-1229Trigonometric Liénard equationWeak focusCyclicityGiven a planar analytic differential equation with a critical point which is a weak focus of order k, it is well known that at most k limit cycles can bifurcate from it. Moreover, in case of analytic Liénard differential equations this order can be computed as one half of the multiplicity of an associated planar analytic map. By using this approach, we can give an upper bound of the maximum order of the weak focus of pure trigonometric Liénard equations only in terms of the degrees of the involved trigonometric polynomials. Our result extends to this trigonometric Liénard case a similar result known for polynomial Liénard equations. 22019-01-0120192019-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/221357https://dx.doi.org/urn:doi:10.1007/s10231-019-00936-8reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2016-77278-PAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 MTM2017-84383-PAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1276open 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:2213572026-06-06T12:50:31Z
dc.title.none.fl_str_mv Highest weak focus order for trigonometric Liénard equations
title Highest weak focus order for trigonometric Liénard equations
spellingShingle Highest weak focus order for trigonometric Liénard equations
Gasull, Armengol|||0000-0002-1719-8231
Trigonometric Liénard equation
Weak focus
Cyclicity
title_short Highest weak focus order for trigonometric Liénard equations
title_full Highest weak focus order for trigonometric Liénard equations
title_fullStr Highest weak focus order for trigonometric Liénard equations
title_full_unstemmed Highest weak focus order for trigonometric Liénard equations
title_sort Highest weak focus order for trigonometric Liénard equations
dc.creator.none.fl_str_mv Gasull, Armengol|||0000-0002-1719-8231
Giné, Jaume|||0000-0001-7109-2553
Valls, Clàudia|||0000-0001-8279-1229
author Gasull, Armengol|||0000-0002-1719-8231
author_facet Gasull, Armengol|||0000-0002-1719-8231
Giné, Jaume|||0000-0001-7109-2553
Valls, Clàudia|||0000-0001-8279-1229
author_role author
author2 Giné, Jaume|||0000-0001-7109-2553
Valls, Clàudia|||0000-0001-8279-1229
author2_role author
author
dc.subject.none.fl_str_mv Trigonometric Liénard equation
Weak focus
Cyclicity
topic Trigonometric Liénard equation
Weak focus
Cyclicity
description Given a planar analytic differential equation with a critical point which is a weak focus of order k, it is well known that at most k limit cycles can bifurcate from it. Moreover, in case of analytic Liénard differential equations this order can be computed as one half of the multiplicity of an associated planar analytic map. By using this approach, we can give an upper bound of the maximum order of the weak focus of pure trigonometric Liénard equations only in terms of the degrees of the involved trigonometric polynomials. Our result extends to this trigonometric Liénard case a similar result known for polynomial Liénard equations.
publishDate 2019
dc.date.none.fl_str_mv 2
2019-01-01
2019
2019-01-01
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/221357
https://dx.doi.org/urn:doi:10.1007/s10231-019-00936-8
url https://ddd.uab.cat/record/221357
https://dx.doi.org/urn:doi:10.1007/s10231-019-00936-8
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 MTM2016-77278-P
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617
Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 MTM2017-84383-P
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1276
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
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869416611626090496
score 15,300719

Similares en LA Referencia