Strongly formal weierstrass non-integrability for polynomial differential systems in C2

Recently a criterion has been given for determining the weakly formal Weierstrass non-integrability of polynomial differential systems in C2. Here we extend this criterion for determining the strongly formal Weierstrass non-integrability which includes the weakly formal Weierstrass non-integrability...

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Autores: Giné, Jaume|||0000-0001-7109-2553, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:221359
Acceso en línea:https://ddd.uab.cat/record/221359
https://dx.doi.org/urn:doi:10.14232/ejqtde.2020.1.1
Access Level:acceso abierto
Palabra clave:Liouville integrability
Polynomial differential systems
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spelling Strongly formal weierstrass non-integrability for polynomial differential systems in C2Giné, Jaume|||0000-0001-7109-2553Llibre, Jaume|||0000-0002-9511-5999Liouville integrabilityPolynomial differential systemsRecently a criterion has been given for determining the weakly formal Weierstrass non-integrability of polynomial differential systems in C2. Here we extend this criterion for determining the strongly formal Weierstrass non-integrability which includes the weakly formal Weierstrass non-integrability of polynomial differential systems in C2. The criterion is based on the solutions of the form y = f(x) with f(x) ∈ C[[x]] of the differential system whose integrability we are studying. The results are applied to a differential system that contains the famous force-free Duffing and the Duffing-Van der Pol oscillators. 22020-01-0120202020-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/221359https://dx.doi.org/urn:doi:10.14232/ejqtde.2020.1.1reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia 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-1276Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-77278-PMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MDM-2014-0445Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617European Commission https://doi.org/10.13039/501100000780 777911open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2213592026-06-06T12:50:31Z
dc.title.none.fl_str_mv Strongly formal weierstrass non-integrability for polynomial differential systems in C2
title Strongly formal weierstrass non-integrability for polynomial differential systems in C2
spellingShingle Strongly formal weierstrass non-integrability for polynomial differential systems in C2
Giné, Jaume|||0000-0001-7109-2553
Liouville integrability
Polynomial differential systems
title_short Strongly formal weierstrass non-integrability for polynomial differential systems in C2
title_full Strongly formal weierstrass non-integrability for polynomial differential systems in C2
title_fullStr Strongly formal weierstrass non-integrability for polynomial differential systems in C2
title_full_unstemmed Strongly formal weierstrass non-integrability for polynomial differential systems in C2
title_sort Strongly formal weierstrass non-integrability for polynomial differential systems in C2
dc.creator.none.fl_str_mv Giné, Jaume|||0000-0001-7109-2553
Llibre, Jaume|||0000-0002-9511-5999
author Giné, Jaume|||0000-0001-7109-2553
author_facet Giné, Jaume|||0000-0001-7109-2553
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 Liouville integrability
Polynomial differential systems
topic Liouville integrability
Polynomial differential systems
description Recently a criterion has been given for determining the weakly formal Weierstrass non-integrability of polynomial differential systems in C2. Here we extend this criterion for determining the strongly formal Weierstrass non-integrability which includes the weakly formal Weierstrass non-integrability of polynomial differential systems in C2. The criterion is based on the solutions of the form y = f(x) with f(x) ∈ C[[x]] of the differential system whose integrability we are studying. The results are applied to a differential system that contains the famous force-free Duffing and the Duffing-Van der Pol oscillators.
publishDate 2020
dc.date.none.fl_str_mv 2
2020-01-01
2020
2020-01-01
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/221359
https://dx.doi.org/urn:doi:10.14232/ejqtde.2020.1.1
url https://ddd.uab.cat/record/221359
https://dx.doi.org/urn:doi:10.14232/ejqtde.2020.1.1
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv 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
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-77278-P
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MDM-2014-0445
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617
European Commission https://doi.org/10.13039/501100000780 777911
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/4.0/
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://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
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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
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collection Dipòsit Digital de Documents de la UAB
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