Polynomial differential systems having a given Darbouxian first integral

The Darbouxian theory of integrability allows to determine when a polynomial differential system in C2 has a first integral of the kind f λ1 1 ···f λp p exp(g/h) where fi , g and h are polynomials in C[x, y], and λi ∈ C for i = 1, . . . ,p. The functions of this form are called Darbouxian functions....

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Detalles Bibliográficos
Autores: Llibre Saló, Jaume, Pantazi, Chara|||0000-0002-4394-404X
Tipo de recurso: artículo
Fecha de publicación:2004
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:2117/1212
Acceso en línea:https://hdl.handle.net/2117/1212
Access Level:acceso abierto
Palabra clave:Differential equations
Polynomial differential system
First integral
Darbouxian function
Equacions diferencials ordinàries
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
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spelling Polynomial differential systems having a given Darbouxian first integralLlibre Saló, JaumePantazi, Chara|||0000-0002-4394-404XDifferential equationsPolynomial differential systemFirst integralDarbouxian functionEquacions diferencials ordinàriesClassificació AMS::34 Ordinary differential equations::34C Qualitative theoryThe Darbouxian theory of integrability allows to determine when a polynomial differential system in C2 has a first integral of the kind f λ1 1 ···f λp p exp(g/h) where fi , g and h are polynomials in C[x, y], and λi ∈ C for i = 1, . . . ,p. The functions of this form are called Darbouxian functions. Here, we solve the inverse problem, i.e. we characterize the polynomial vector fields in C2 having a given Darbouxian function as a first integral. On the other hand, using information about the degree of the invariant algebraic curves of a polynomial vector field, we improve the conditions for the existence of an integrating factor in the Darbouxian theory of integrability.Peer ReviewedElsevier20042004-01-0120072007-10-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/1212reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/12122026-05-27T15:37:01Z
dc.title.none.fl_str_mv Polynomial differential systems having a given Darbouxian first integral
title Polynomial differential systems having a given Darbouxian first integral
spellingShingle Polynomial differential systems having a given Darbouxian first integral
Llibre Saló, Jaume
Differential equations
Polynomial differential system
First integral
Darbouxian function
Equacions diferencials ordinàries
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
title_short Polynomial differential systems having a given Darbouxian first integral
title_full Polynomial differential systems having a given Darbouxian first integral
title_fullStr Polynomial differential systems having a given Darbouxian first integral
title_full_unstemmed Polynomial differential systems having a given Darbouxian first integral
title_sort Polynomial differential systems having a given Darbouxian first integral
dc.creator.none.fl_str_mv Llibre Saló, Jaume
Pantazi, Chara|||0000-0002-4394-404X
author Llibre Saló, Jaume
author_facet Llibre Saló, Jaume
Pantazi, Chara|||0000-0002-4394-404X
author_role author
author2 Pantazi, Chara|||0000-0002-4394-404X
author2_role author
dc.subject.none.fl_str_mv Differential equations
Polynomial differential system
First integral
Darbouxian function
Equacions diferencials ordinàries
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
topic Differential equations
Polynomial differential system
First integral
Darbouxian function
Equacions diferencials ordinàries
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
description The Darbouxian theory of integrability allows to determine when a polynomial differential system in C2 has a first integral of the kind f λ1 1 ···f λp p exp(g/h) where fi , g and h are polynomials in C[x, y], and λi ∈ C for i = 1, . . . ,p. The functions of this form are called Darbouxian functions. Here, we solve the inverse problem, i.e. we characterize the polynomial vector fields in C2 having a given Darbouxian function as a first integral. On the other hand, using information about the degree of the invariant algebraic curves of a polynomial vector field, we improve the conditions for the existence of an integrating factor in the Darbouxian theory of integrability.
publishDate 2004
dc.date.none.fl_str_mv 2004
2004-01-01
2007
2007-10-01
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/2117/1212
url https://hdl.handle.net/2117/1212
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
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
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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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