Analytic reducibility of nondegenerate centers: Cherkas systems

In this paper we study the center problem for polynomial differential systems and we prove that any center of an analytic differential system is analytically reducible. x˙=y,y˙=P0(x)+P1(x)y+P2(x)y2, We also study the centers for the Cherkas polynomial differential systems where Pi(x) are polynomials...

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Detalhes bibliográficos
Autores: Giné, Jaume, Llibre, Jaume
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2016
País:España
Recursos:Universitat de Lleida (UdL)
Repositório:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/59108
Acesso em linha:https://doi.org/10.14232/ejqtde.2016.1.49
http://hdl.handle.net/10459.1/59108
Access Level:Acceso aberto
Palavra-chave:Center problem
Analytic integrability
Polynomial Cherkas differential systems
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spelling Analytic reducibility of nondegenerate centers: Cherkas systemsGiné, JaumeLlibre, JaumeCenter problemAnalytic integrabilityPolynomial Cherkas differential systemsIn this paper we study the center problem for polynomial differential systems and we prove that any center of an analytic differential system is analytically reducible. x˙=y,y˙=P0(x)+P1(x)y+P2(x)y2, We also study the centers for the Cherkas polynomial differential systems where Pi(x) are polynomials of degree n, P0(0)=0 and P′0(0)<0. Computing the focal values we find the center conditions for such systems for degree 3, and using modular arithmetics for degree 4. Finally we do a conjecture about the center conditions for Cherkas polynomial differential systems of degree n.The first author is partially supported by a MINECO/FEDER grant number MTM2014-53703-P and an AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204. The second author is partially supported by a MINECO grant MTM2013-40998-P, an AGAUR grant 2014SGR 568, and two grants FP7-PEOPLE-2012-IRSES numbers 316338 and 318999.Bolyai Institute, University of SzegedHungarian Academy of Sciences2016info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://doi.org/10.14232/ejqtde.2016.1.49http://hdl.handle.net/10459.1/59108reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)Inglésinfo:eu-repo/grantAgreement/MINECO//MTM2014-53703-Pinfo:eu-repo/grantAgreement/MINECO//MTM2013-40998-PReproducció del document publicat a https://doi.org/10.14232/ejqtde.2016.1.49Electronic Journal of Qualitative Theory of Differential Equations, 2016, núm. 49, p. 1–10info:eu-repo/grantAgreement/EC/FP7/316338info:eu-repo/grantAgreement/EC/FP7/318999cc-by (c) Giné, Jaume et al., 2016info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/4.0/deed.es_ESoai:repositori.udl.cat:10459.1/591082026-06-24T12:42:17Z
dc.title.none.fl_str_mv Analytic reducibility of nondegenerate centers: Cherkas systems
title Analytic reducibility of nondegenerate centers: Cherkas systems
spellingShingle Analytic reducibility of nondegenerate centers: Cherkas systems
Giné, Jaume
Center problem
Analytic integrability
Polynomial Cherkas differential systems
title_short Analytic reducibility of nondegenerate centers: Cherkas systems
title_full Analytic reducibility of nondegenerate centers: Cherkas systems
title_fullStr Analytic reducibility of nondegenerate centers: Cherkas systems
title_full_unstemmed Analytic reducibility of nondegenerate centers: Cherkas systems
title_sort Analytic reducibility of nondegenerate centers: Cherkas systems
dc.creator.none.fl_str_mv Giné, Jaume
Llibre, Jaume
author Giné, Jaume
author_facet Giné, Jaume
Llibre, Jaume
author_role author
author2 Llibre, Jaume
author2_role author
dc.subject.none.fl_str_mv Center problem
Analytic integrability
Polynomial Cherkas differential systems
topic Center problem
Analytic integrability
Polynomial Cherkas differential systems
description In this paper we study the center problem for polynomial differential systems and we prove that any center of an analytic differential system is analytically reducible. x˙=y,y˙=P0(x)+P1(x)y+P2(x)y2, We also study the centers for the Cherkas polynomial differential systems where Pi(x) are polynomials of degree n, P0(0)=0 and P′0(0)<0. Computing the focal values we find the center conditions for such systems for degree 3, and using modular arithmetics for degree 4. Finally we do a conjecture about the center conditions for Cherkas polynomial differential systems of degree n.
publishDate 2016
dc.date.none.fl_str_mv 2016
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/10.14232/ejqtde.2016.1.49
http://hdl.handle.net/10459.1/59108
url https://doi.org/10.14232/ejqtde.2016.1.49
http://hdl.handle.net/10459.1/59108
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MINECO//MTM2014-53703-P
info:eu-repo/grantAgreement/MINECO//MTM2013-40998-P
Reproducció del document publicat a https://doi.org/10.14232/ejqtde.2016.1.49
Electronic Journal of Qualitative Theory of Differential Equations, 2016, núm. 49, p. 1–10
info:eu-repo/grantAgreement/EC/FP7/316338
info:eu-repo/grantAgreement/EC/FP7/318999
dc.rights.none.fl_str_mv cc-by (c) Giné, Jaume et al., 2016
info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/4.0/deed.es_ES
rights_invalid_str_mv cc-by (c) Giné, Jaume et al., 2016
https://creativecommons.org/licenses/by/4.0/deed.es_ES
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Bolyai Institute, University of Szeged
Hungarian Academy of Sciences
publisher.none.fl_str_mv Bolyai Institute, University of Szeged
Hungarian Academy of Sciences
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
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.811543

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