Integrability Conditions for Complex Homogeneous Kukles Systems

In this paper we study the existence of local analytic first integrals for complex polynomial differential systems of the form ẋ = x + Pn(x, y), ẏ = −y, where Pn(x,y) is a homogeneous polynomial of degree n, called the complex homogeneous Kukles systems of degree n. We characterize all the homogeneo...

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Detalles Bibliográficos
Autores: Giné, Jaume, Valls, Claudia
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2018
País:España
Institución:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/72807
Acceso en línea:https://doi.org/10.1080/14029251.2018.1494731
http://hdl.handle.net/10459.1/72807
Access Level:acceso abierto
Palabra clave:Integrability
Complex center-focus problem
Saddle constants
Kukles systems
Gröbner Basis
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spelling Integrability Conditions for Complex Homogeneous Kukles SystemsGiné, JaumeValls, ClaudiaIntegrabilityComplex center-focus problemSaddle constantsKukles systemsGröbner BasisIn this paper we study the existence of local analytic first integrals for complex polynomial differential systems of the form ẋ = x + Pn(x, y), ẏ = −y, where Pn(x,y) is a homogeneous polynomial of degree n, called the complex homogeneous Kukles systems of degree n. We characterize all the homogeneous Kukles systems of degree n that belong to the Sibirsky ideal. Finally, we provide necessary and sufficient conditions when n = 2,...,7 in order that the complex homogeneous Kukles system has a local analytic first integral computing the saddle constants and using Gröbner bases to find the decomposition of the algebraic variety into its irreducible components.The first author is partially supported by a MINECO/ FEDER grant number 2017-84383-P and an AGAUR (Generalitat de Catalunya) grant number 2017SGR 1276. The second author is partially supported by FCT/Portugal through UID/MAT/04459/2013.Atlantis and Taylor & Francis2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://doi.org/10.1080/14029251.2018.1494731http://hdl.handle.net/10459.1/72807reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)InglésReproducció del document publicat a https://doi.org/10.1080/14029251.2018.1494731Journal of Nonlinear Mathematical Physics, 2018, vol. 25, núm. 3, p. 387-398cc-by-nc (c) Jaume Giné, Claudia Valls, 2018info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc/4.0/oai:repositori.udl.cat:10459.1/728072026-06-24T12:42:17Z
dc.title.none.fl_str_mv Integrability Conditions for Complex Homogeneous Kukles Systems
title Integrability Conditions for Complex Homogeneous Kukles Systems
spellingShingle Integrability Conditions for Complex Homogeneous Kukles Systems
Giné, Jaume
Integrability
Complex center-focus problem
Saddle constants
Kukles systems
Gröbner Basis
title_short Integrability Conditions for Complex Homogeneous Kukles Systems
title_full Integrability Conditions for Complex Homogeneous Kukles Systems
title_fullStr Integrability Conditions for Complex Homogeneous Kukles Systems
title_full_unstemmed Integrability Conditions for Complex Homogeneous Kukles Systems
title_sort Integrability Conditions for Complex Homogeneous Kukles Systems
dc.creator.none.fl_str_mv Giné, Jaume
Valls, Claudia
author Giné, Jaume
author_facet Giné, Jaume
Valls, Claudia
author_role author
author2 Valls, Claudia
author2_role author
dc.subject.none.fl_str_mv Integrability
Complex center-focus problem
Saddle constants
Kukles systems
Gröbner Basis
topic Integrability
Complex center-focus problem
Saddle constants
Kukles systems
Gröbner Basis
description In this paper we study the existence of local analytic first integrals for complex polynomial differential systems of the form ẋ = x + Pn(x, y), ẏ = −y, where Pn(x,y) is a homogeneous polynomial of degree n, called the complex homogeneous Kukles systems of degree n. We characterize all the homogeneous Kukles systems of degree n that belong to the Sibirsky ideal. Finally, we provide necessary and sufficient conditions when n = 2,...,7 in order that the complex homogeneous Kukles system has a local analytic first integral computing the saddle constants and using Gröbner bases to find the decomposition of the algebraic variety into its irreducible components.
publishDate 2018
dc.date.none.fl_str_mv 2018
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/10.1080/14029251.2018.1494731
http://hdl.handle.net/10459.1/72807
url https://doi.org/10.1080/14029251.2018.1494731
http://hdl.handle.net/10459.1/72807
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a https://doi.org/10.1080/14029251.2018.1494731
Journal of Nonlinear Mathematical Physics, 2018, vol. 25, núm. 3, p. 387-398
dc.rights.none.fl_str_mv cc-by-nc (c) Jaume Giné, Claudia Valls, 2018
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc/4.0/
rights_invalid_str_mv cc-by-nc (c) Jaume Giné, Claudia Valls, 2018
http://creativecommons.org/licenses/by-nc/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Atlantis and Taylor & Francis
publisher.none.fl_str_mv Atlantis and Taylor & Francis
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 15.812429

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