Psi-series of quadratic vector fields on the plane

Psi-series (i.e., logarithmic series) for the solutions of quadratic vector fields on the plane are considered. Its existence and convergence is studied, and an algorithm for the location of logarithmic singularities is developed. Moreover, the relationship between psi-series and non-integrability i...

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Detalles Bibliográficos
Autores: Delshams Valdés, Amadeu|||0000-0003-4134-8882, Mir, Arnau
Tipo de recurso: artículo
Fecha de publicación:1997
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/875
Acceso en línea:https://hdl.handle.net/2117/875
Access Level:acceso abierto
Palabra clave:Differential equations
Equacions diferencials ordinàries
Classificació AMS::34 Ordinary differential equations::34A General theory
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spelling Psi-series of quadratic vector fields on the planeDelshams Valdés, Amadeu|||0000-0003-4134-8882Mir, ArnauDifferential equationsEquacions diferencials ordinàriesEquacions diferencials ordinàriesClassificació AMS::34 Ordinary differential equations::34A General theoryPsi-series (i.e., logarithmic series) for the solutions of quadratic vector fields on the plane are considered. Its existence and convergence is studied, and an algorithm for the location of logarithmic singularities is developed. Moreover, the relationship between psi-series and non-integrability is stressed and in particular it is proved that quadratic systems with psi-series that are not Laurent series do not have an algebraic first integral. Besides, a criterion about non-existence of an analytic first integral is given.19971997-01-0120072007-05-04journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/875reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 2.5 Spainhttp://creativecommons.org/licenses/by-nc-nd/2.5/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/8752026-05-27T15:37:01Z
dc.title.none.fl_str_mv Psi-series of quadratic vector fields on the plane
title Psi-series of quadratic vector fields on the plane
spellingShingle Psi-series of quadratic vector fields on the plane
Delshams Valdés, Amadeu|||0000-0003-4134-8882
Differential equations
Equacions diferencials ordinàries
Equacions diferencials ordinàries
Classificació AMS::34 Ordinary differential equations::34A General theory
title_short Psi-series of quadratic vector fields on the plane
title_full Psi-series of quadratic vector fields on the plane
title_fullStr Psi-series of quadratic vector fields on the plane
title_full_unstemmed Psi-series of quadratic vector fields on the plane
title_sort Psi-series of quadratic vector fields on the plane
dc.creator.none.fl_str_mv Delshams Valdés, Amadeu|||0000-0003-4134-8882
Mir, Arnau
author Delshams Valdés, Amadeu|||0000-0003-4134-8882
author_facet Delshams Valdés, Amadeu|||0000-0003-4134-8882
Mir, Arnau
author_role author
author2 Mir, Arnau
author2_role author
dc.subject.none.fl_str_mv Differential equations
Equacions diferencials ordinàries
Equacions diferencials ordinàries
Classificació AMS::34 Ordinary differential equations::34A General theory
topic Differential equations
Equacions diferencials ordinàries
Equacions diferencials ordinàries
Classificació AMS::34 Ordinary differential equations::34A General theory
description Psi-series (i.e., logarithmic series) for the solutions of quadratic vector fields on the plane are considered. Its existence and convergence is studied, and an algorithm for the location of logarithmic singularities is developed. Moreover, the relationship between psi-series and non-integrability is stressed and in particular it is proved that quadratic systems with psi-series that are not Laurent series do not have an algebraic first integral. Besides, a criterion about non-existence of an analytic first integral is given.
publishDate 1997
dc.date.none.fl_str_mv 1997
1997-01-01
2007
2007-05-04
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/875
url https://hdl.handle.net/2117/875
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
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300724

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