Global centers of a class of cubic polynomial differential systems

Bibliographic Details
Main Author: Llibre, Jaume
Publication Date: 2024
Other Authors: Rondón, Gabriel [UNESP]
Format: Article
Language: eng
Source: Repositório Institucional da UNESP
Download full: http://dx.doi.org/10.1007/s12215-024-01034-2
https://hdl.handle.net/11449/299852
Summary: A difficult classical problem in the qualitative theory of differential systems in the plane R2 is the center-focus problem, i.e. to distinguish between a focus and a center. Another difficult problem is to distinguish inside a family of centers the ones which are global. A global center is a center p such that R2\{p} is filled with periodic orbits. In this paper we classify the global centers of the family of real polynomial differential systems of degree 3 that in complex notation write (Formula presented.) where w=x+iy and Ak∈C for k=3,4,5,6.
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spelling Global centers of a class of cubic polynomial differential systems34C05Global centersPolynomial differential equationsVertical blow-upA difficult classical problem in the qualitative theory of differential systems in the plane R2 is the center-focus problem, i.e. to distinguish between a focus and a center. Another difficult problem is to distinguish inside a family of centers the ones which are global. A global center is a center p such that R2\{p} is filled with periodic orbits. In this paper we classify the global centers of the family of real polynomial differential systems of degree 3 that in complex notation write (Formula presented.) where w=x+iy and Ak∈C for k=3,4,5,6.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Agència de Gestió d'Ajuts Universitaris i de RecercaH2020 European Research CouncilAgencia Estatal de InvestigaciónDepartament de Matemàtiques Edifici Cc Universitat Autònoma de Barcelona, CataloniaInstitute of Biosciences Humanities and Exact Sciences São Paulo State University (Unesp), Rua C. Colombo, 2265, São PauloInstitute of Biosciences Humanities and Exact Sciences São Paulo State University (Unesp), Rua C. Colombo, 2265, São PauloFAPESP: 2020/06708-9Agència de Gestió d'Ajuts Universitaris i de Recerca: 2021SGR00113FAPESP: 2022/12123-9H2020 European Research Council: MSCA-RISE-2017-777911Agencia Estatal de Investigación: PID2019- 104658GB-I00Universitat Autònoma de BarcelonaUniversidade Estadual Paulista (UNESP)Llibre, JaumeRondón, Gabriel [UNESP]2025-04-29T18:47:58Z2024-08-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article2141-2160http://dx.doi.org/10.1007/s12215-024-01034-2Rendiconti del Circolo Matematico di Palermo, v. 73, n. 5, p. 2141-2160, 2024.1973-44090009-725Xhttps://hdl.handle.net/11449/29985210.1007/s12215-024-01034-22-s2.0-85191489726Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengRendiconti del Circolo Matematico di Palermoinfo:eu-repo/semantics/openAccess2025-04-30T13:42:01Zoai:repositorio.unesp.br:11449/299852Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462025-04-30T13:42:01Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Global centers of a class of cubic polynomial differential systems
title Global centers of a class of cubic polynomial differential systems
spellingShingle Global centers of a class of cubic polynomial differential systems
Llibre, Jaume
34C05
Global centers
Polynomial differential equations
Vertical blow-up
title_short Global centers of a class of cubic polynomial differential systems
title_full Global centers of a class of cubic polynomial differential systems
title_fullStr Global centers of a class of cubic polynomial differential systems
title_full_unstemmed Global centers of a class of cubic polynomial differential systems
title_sort Global centers of a class of cubic polynomial differential systems
author Llibre, Jaume
author_facet Llibre, Jaume
Rondón, Gabriel [UNESP]
author_role author
author2 Rondón, Gabriel [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universitat Autònoma de Barcelona
Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Llibre, Jaume
Rondón, Gabriel [UNESP]
dc.subject.por.fl_str_mv 34C05
Global centers
Polynomial differential equations
Vertical blow-up
topic 34C05
Global centers
Polynomial differential equations
Vertical blow-up
description A difficult classical problem in the qualitative theory of differential systems in the plane R2 is the center-focus problem, i.e. to distinguish between a focus and a center. Another difficult problem is to distinguish inside a family of centers the ones which are global. A global center is a center p such that R2\{p} is filled with periodic orbits. In this paper we classify the global centers of the family of real polynomial differential systems of degree 3 that in complex notation write (Formula presented.) where w=x+iy and Ak∈C for k=3,4,5,6.
publishDate 2024
dc.date.none.fl_str_mv 2024-08-01
2025-04-29T18:47:58Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1007/s12215-024-01034-2
Rendiconti del Circolo Matematico di Palermo, v. 73, n. 5, p. 2141-2160, 2024.
1973-4409
0009-725X
https://hdl.handle.net/11449/299852
10.1007/s12215-024-01034-2
2-s2.0-85191489726
url http://dx.doi.org/10.1007/s12215-024-01034-2
https://hdl.handle.net/11449/299852
identifier_str_mv Rendiconti del Circolo Matematico di Palermo, v. 73, n. 5, p. 2141-2160, 2024.
1973-4409
0009-725X
10.1007/s12215-024-01034-2
2-s2.0-85191489726
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Rendiconti del Circolo Matematico di Palermo
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 2141-2160
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv repositoriounesp@unesp.br
_version_ 1834482496556761088

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