Quadratic systems with a rational first integral of degree three

A quadratic polynomial differential system can be identified with a single point of R12 through its coefficients. The phase portrait of the quadratic systems having a rational first integral of degree 3 have been studied using normal forms. Here using the algebraic invariant theory, we characterize...

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Autores: Artés Ferragud, Joan Carles|||0000-0003-4332-7495, Llibre, Jaume|||0000-0002-9511-5999, Vulpe, Nicolae
Tipo de recurso: artículo
Fecha de publicación:2010
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:226092
Acceso en línea:https://ddd.uab.cat/record/226092
https://dx.doi.org/urn:doi:10.1007/s12215-010-0032-0
Access Level:acceso abierto
Palabra clave:Quadratic vector fields
Integrability
Rational first integral
Phase portraits
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spelling Quadratic systems with a rational first integral of degree threeA complete classification in the coefficient space R12Artés Ferragud, Joan Carles|||0000-0003-4332-7495Llibre, Jaume|||0000-0002-9511-5999Vulpe, NicolaeQuadratic vector fieldsIntegrabilityRational first integralPhase portraitsA quadratic polynomial differential system can be identified with a single point of R12 through its coefficients. The phase portrait of the quadratic systems having a rational first integral of degree 3 have been studied using normal forms. Here using the algebraic invariant theory, we characterize all the non-degenerate quadratic polynomial differential systems in R12 having a rational first integral of degree 3. We show that there are only 31 different topological phase portraits in the Poincaré disc associated to this family of quadratic systems up to a reversal of the sense of their orbits, and we provide representatives of every class modulo an affine change of variables and a rescaling of the time variable. Moreover, each one of these 31 representatives is determined by a set of algebraic invariant conditions and we provide for it a first integral. 22010-01-0120102010-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/226092https://dx.doi.org/urn:doi:10.1007/s12215-010-0032-0reponame: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 2001/SGR-00173open 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:2260922026-06-06T12:50:31Z
dc.title.none.fl_str_mv Quadratic systems with a rational first integral of degree three
A complete classification in the coefficient space R12
title Quadratic systems with a rational first integral of degree three
spellingShingle Quadratic systems with a rational first integral of degree three
Artés Ferragud, Joan Carles|||0000-0003-4332-7495
Quadratic vector fields
Integrability
Rational first integral
Phase portraits
title_short Quadratic systems with a rational first integral of degree three
title_full Quadratic systems with a rational first integral of degree three
title_fullStr Quadratic systems with a rational first integral of degree three
title_full_unstemmed Quadratic systems with a rational first integral of degree three
title_sort Quadratic systems with a rational first integral of degree three
dc.creator.none.fl_str_mv Artés Ferragud, Joan Carles|||0000-0003-4332-7495
Llibre, Jaume|||0000-0002-9511-5999
Vulpe, Nicolae
author Artés Ferragud, Joan Carles|||0000-0003-4332-7495
author_facet Artés Ferragud, Joan Carles|||0000-0003-4332-7495
Llibre, Jaume|||0000-0002-9511-5999
Vulpe, Nicolae
author_role author
author2 Llibre, Jaume|||0000-0002-9511-5999
Vulpe, Nicolae
author2_role author
author
dc.subject.none.fl_str_mv Quadratic vector fields
Integrability
Rational first integral
Phase portraits
topic Quadratic vector fields
Integrability
Rational first integral
Phase portraits
description A quadratic polynomial differential system can be identified with a single point of R12 through its coefficients. The phase portrait of the quadratic systems having a rational first integral of degree 3 have been studied using normal forms. Here using the algebraic invariant theory, we characterize all the non-degenerate quadratic polynomial differential systems in R12 having a rational first integral of degree 3. We show that there are only 31 different topological phase portraits in the Poincaré disc associated to this family of quadratic systems up to a reversal of the sense of their orbits, and we provide representatives of every class modulo an affine change of variables and a rescaling of the time variable. Moreover, each one of these 31 representatives is determined by a set of algebraic invariant conditions and we provide for it a first integral.
publishDate 2010
dc.date.none.fl_str_mv 2
2010-01-01
2010
2010-01-01
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
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dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/226092
https://dx.doi.org/urn:doi:10.1007/s12215-010-0032-0
url https://ddd.uab.cat/record/226092
https://dx.doi.org/urn:doi:10.1007/s12215-010-0032-0
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 2001/SGR-00173
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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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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