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...

Descripción completa

Detalles Bibliográficos
Autores: García, I. A. (Isaac A.), Llibre, Jaume
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.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
id ES_85f34bc019edf2a31ac708a169be9521
oai_identifier_str oai:recercat.cat:10459.1/85031
network_acronym_str ES
network_name_str España
repository_id_str
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-2017-777911Springer202220222023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://doi.org/10.1007/s12215-022-00850-8http://hdl.handle.net/10459.1/85031http://hdl.handle.net/10459.1/85031reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)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:recercat.cat:10459.1/850312026-05-29T05:05:01Z
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 2022
dc.date.none.fl_str_mv 2022
2022
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
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:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869412338219614208
score 15.811543

Similares en LA Referencia