The center problem for a family of systems of differential equations having a nilpotent singular point

We study the analytic system of differential equations in the plane(over(x, ̇), over(y, ̇))t = underover(∑, i = 0, ∞) Fq - p + 2 i s, where p, q ∈ N, p ≤ q, s = (n + 1) p - q > 0, n ∈ N, and Fi = (Pi, Qi)t are quasi-homogeneous vector fields of type t = (p, q) and degree i, with Fq - p = (y,...

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Detalles Bibliográficos
Autores: Algaba Durán, Antonio, García García, Cristóbal, Reyes Columé, Manuel
Tipo de recurso: artículo
Fecha de publicación:2008
País:España
Institución:Universidad de Huelva (UHU)
Repositorio:Arias Montano. Repositorio Institucional de la Universidad de Huelva
Idioma:inglés
OAI Identifier:oai:ariasmontano.uhu.es:10272/25434
Acceso en línea:https://hdl.handle.net/10272/25434
Access Level:acceso abierto
Palabra clave:Centers
Nilpotent and monodromic singular point
Lyapunov function
12 Matemáticas
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spelling The center problem for a family of systems of differential equations having a nilpotent singular pointAlgaba Durán, AntonioGarcía García, CristóbalReyes Columé, ManuelCentersNilpotent and monodromic singular pointLyapunov function12 MatemáticasWe study the analytic system of differential equations in the plane(over(x, ̇), over(y, ̇))t = underover(∑, i = 0, ∞) Fq - p + 2 i s, where p, q ∈ N, p ≤ q, s = (n + 1) p - q > 0, n ∈ N, and Fi = (Pi, Qi)t are quasi-homogeneous vector fields of type t = (p, q) and degree i, with Fq - p = (y, 0)t and Qq - p + 2 s (1, 0) < 0. The origin of this system is a nilpotent and monodromic isolated singular point. We prove for this system the existence of a Lyapunov function and we solve theoretically the center problem for such system. Finally, as an application of the theoretical procedure, we characterize the centers of several subfamiliesElsevier20082008-04-0120082008-04-01journal articlehttp://purl.org/coar/resource_type/c_6501SMURhttp://purl.org/coar/version/c_71e4c1898caa6e32info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10272/25434reponame:Arias Montano. Repositorio Institucional de la Universidad de Huelvainstname:Universidad de Huelva (UHU)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Atribución-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nd/3.0/es/info:eu-repo/semantics/openAccessoai:ariasmontano.uhu.es:10272/254342026-06-02T14:58:11Z
dc.title.none.fl_str_mv The center problem for a family of systems of differential equations having a nilpotent singular point
title The center problem for a family of systems of differential equations having a nilpotent singular point
spellingShingle The center problem for a family of systems of differential equations having a nilpotent singular point
Algaba Durán, Antonio
Centers
Nilpotent and monodromic singular point
Lyapunov function
12 Matemáticas
title_short The center problem for a family of systems of differential equations having a nilpotent singular point
title_full The center problem for a family of systems of differential equations having a nilpotent singular point
title_fullStr The center problem for a family of systems of differential equations having a nilpotent singular point
title_full_unstemmed The center problem for a family of systems of differential equations having a nilpotent singular point
title_sort The center problem for a family of systems of differential equations having a nilpotent singular point
dc.creator.none.fl_str_mv Algaba Durán, Antonio
García García, Cristóbal
Reyes Columé, Manuel
author Algaba Durán, Antonio
author_facet Algaba Durán, Antonio
García García, Cristóbal
Reyes Columé, Manuel
author_role author
author2 García García, Cristóbal
Reyes Columé, Manuel
author2_role author
author
dc.contributor.none.fl_str_mv
dc.subject.none.fl_str_mv Centers
Nilpotent and monodromic singular point
Lyapunov function
12 Matemáticas
topic Centers
Nilpotent and monodromic singular point
Lyapunov function
12 Matemáticas
description We study the analytic system of differential equations in the plane(over(x, ̇), over(y, ̇))t = underover(∑, i = 0, ∞) Fq - p + 2 i s, where p, q ∈ N, p ≤ q, s = (n + 1) p - q > 0, n ∈ N, and Fi = (Pi, Qi)t are quasi-homogeneous vector fields of type t = (p, q) and degree i, with Fq - p = (y, 0)t and Qq - p + 2 s (1, 0) < 0. The origin of this system is a nilpotent and monodromic isolated singular point. We prove for this system the existence of a Lyapunov function and we solve theoretically the center problem for such system. Finally, as an application of the theoretical procedure, we characterize the centers of several subfamilies
publishDate 2008
dc.date.none.fl_str_mv 2008
2008-04-01
2008
2008-04-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
SMUR
http://purl.org/coar/version/c_71e4c1898caa6e32
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10272/25434
url https://hdl.handle.net/10272/25434
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
Atribución-SinDerivadas 3.0 España
http://creativecommons.org/licenses/by-nd/3.0/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
Atribución-SinDerivadas 3.0 España
http://creativecommons.org/licenses/by-nd/3.0/es/
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:Arias Montano. Repositorio Institucional de la Universidad de Huelva
instname:Universidad de Huelva (UHU)
instname_str Universidad de Huelva (UHU)
reponame_str Arias Montano. Repositorio Institucional de la Universidad de Huelva
collection Arias Montano. Repositorio Institucional de la Universidad de Huelva
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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