Polynomial Liénard systems with a nilpotent global center

A center for a differential system x˙=f(x) in R2 is a singular point p having a neighborhood U such that U∖{p} is filled with periodic orbits. A global center is a center p such that R2∖{p} is filled with periodic orbits. There are three kinds of centers, the centers p such that the Jacobian matrix...

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Detalles Bibliográficos
Autores: García, I. A. (Isaac A.), Llibre, Jaume
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/85031
Acceso en línea:https://doi.org/10.1007/s12215-022-00850-8
http://hdl.handle.net/10459.1/85031
Access Level:acceso abierto
Palabra clave:Center
Global center
Periodic orbits
Nilpotent singularity
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spelling Polynomial Liénard systems with a nilpotent global centerGarcía, I. A. (Isaac A.)Llibre, JaumeCenterGlobal centerPeriodic orbitsNilpotent singularityA center for a differential system x˙=f(x) in R2 is a singular point p having a neighborhood U such that U∖{p} is filled with periodic orbits. A global center is a center p such that R2∖{p} is filled with periodic orbits. There are three kinds of centers, the centers p such that the Jacobian matrix Df(p) has purely imaginary eigenvalues, the nilpotent centers p such that Df(p) is a nilpotent matrix, and the degenerate centers p such that the matrix Df(p) is the zero matrix. For the first class of centers there are several works studying when such centers are global. As far as we know there are no works for studying the nilpotent global centers. One of the most studied classes of differential systems in R2 are the polynomial Liénard differential systems. The objective of this paper is to study the nilpotent global centers of the polynomial Liénard differential systems.The first author is partially supported by a MICIN Grant Number PID2020-113758GB-I00 and an AGAUR Grant Number 2017SGR-1276. The second author is partially supported by the Agencia Estatal de Investigación grant PID2019-104658GB-I00, and the H2020 European Research Council Grant MSCA-RISE-2017-777911Springer2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://doi.org/10.1007/s12215-022-00850-8http://hdl.handle.net/10459.1/85031reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)Inglésinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-104658GB-I00info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113758GB-I00Reproducció del document publicat a https://doi.org/10.1007/s12215-022-00850-8Rendiconti del Circolo Matematico di Palermo Series 2, 2023, vol. 72, p. 3625–3636info:eu-repo/grantAgreement/EC/H2020/777911cc-by (c) Isaac A. García, Jaume Llibre, 2023info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/oai:repositori.udl.cat:10459.1/850312026-06-24T12:42:17Z
dc.title.none.fl_str_mv Polynomial Liénard systems with a nilpotent global center
title Polynomial Liénard systems with a nilpotent global center
spellingShingle Polynomial Liénard systems with a nilpotent global center
García, I. A. (Isaac A.)
Center
Global center
Periodic orbits
Nilpotent singularity
title_short Polynomial Liénard systems with a nilpotent global center
title_full Polynomial Liénard systems with a nilpotent global center
title_fullStr Polynomial Liénard systems with a nilpotent global center
title_full_unstemmed Polynomial Liénard systems with a nilpotent global center
title_sort Polynomial Liénard systems with a nilpotent global center
dc.creator.none.fl_str_mv García, I. A. (Isaac A.)
Llibre, Jaume
author García, I. A. (Isaac A.)
author_facet García, I. A. (Isaac A.)
Llibre, Jaume
author_role author
author2 Llibre, Jaume
author2_role author
dc.subject.none.fl_str_mv Center
Global center
Periodic orbits
Nilpotent singularity
topic Center
Global center
Periodic orbits
Nilpotent singularity
description A center for a differential system x˙=f(x) in R2 is a singular point p having a neighborhood U such that U∖{p} is filled with periodic orbits. A global center is a center p such that R2∖{p} is filled with periodic orbits. There are three kinds of centers, the centers p such that the Jacobian matrix Df(p) has purely imaginary eigenvalues, the nilpotent centers p such that Df(p) is a nilpotent matrix, and the degenerate centers p such that the matrix Df(p) is the zero matrix. For the first class of centers there are several works studying when such centers are global. As far as we know there are no works for studying the nilpotent global centers. One of the most studied classes of differential systems in R2 are the polynomial Liénard differential systems. The objective of this paper is to study the nilpotent global centers of the polynomial Liénard differential systems.
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://doi.org/10.1007/s12215-022-00850-8
http://hdl.handle.net/10459.1/85031
url https://doi.org/10.1007/s12215-022-00850-8
http://hdl.handle.net/10459.1/85031
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-104658GB-I00
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113758GB-I00
Reproducció del document publicat a https://doi.org/10.1007/s12215-022-00850-8
Rendiconti del Circolo Matematico di Palermo Series 2, 2023, vol. 72, p. 3625–3636
info:eu-repo/grantAgreement/EC/H2020/777911
dc.rights.none.fl_str_mv cc-by (c) Isaac A. García, Jaume Llibre, 2023
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
rights_invalid_str_mv cc-by (c) Isaac A. García, Jaume Llibre, 2023
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Repositori Obert UdL
instname:Universitat de Lleida (UdL)
instname_str Universitat de Lleida (UdL)
reponame_str Repositori Obert UdL
collection Repositori Obert UdL
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