A NOTE ON HILBERT 16TH PROBLEM

Bibliographic Details
Main Author: Gasull, Armengol
Publication Date: 2025
Other Authors: Santana, Paulo [UNESP]
Format: Article
Language: eng
Source: Repositório Institucional da UNESP
Download full: http://dx.doi.org/10.1090/proc/17116
https://hdl.handle.net/11449/301426
Summary: Let H(n) be the maximum number of limit cycles that a planar polynomial vector field of degree n can have. In this paper we prove that H(n) is realizable by structurally stable vector fields with only hyperbolic limit cycles and that it is a strictly increasing function whenever it is finite.
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spelling A NOTE ON HILBERT 16TH PROBLEMHilbert 16th problemlimit cyclesstructurally stable vector fieldsLet H(n) be the maximum number of limit cycles that a planar polynomial vector field of degree n can have. In this paper we prove that H(n) is realizable by structurally stable vector fields with only hyperbolic limit cycles and that it is a strictly increasing function whenever it is finite.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Agència de Gestió d'Ajuts Universitaris i de RecercaCentre of Excellence in Cognition and its Disorders, Australian Research CouncilAgencia Estatal de InvestigaciónDepartament de MatemàtiQues Facultat de Ciències Universitat Autònoma de Barcelona, BellaterraCentre de Recerca Matemàtica Edifici Cc, Campus de Bellaterra, Cerdanyola del VallèsIBILCE–UNESP, S. J. Rio PretoIBILCE–UNESP, S. J. Rio PretoFAPESP: 2019/10269-3Agència de Gestió d'Ajuts Universitaris i de Recerca: 2021-SGR-00113FAPESP: 2021/01799-9FAPESP: 2022/14353-1Centre of Excellence in Cognition and its Disorders, Australian Research Council: CEX2020-001084-MAgencia Estatal de Investigación: PID2022-136613NB-I00Universitat Autònoma de BarcelonaEdifici CcUniversidade Estadual Paulista (UNESP)Gasull, ArmengolSantana, Paulo [UNESP]2025-04-29T18:58:10Z2025-02-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article669-677http://dx.doi.org/10.1090/proc/17116Proceedings of the American Mathematical Society, v. 153, n. 2, p. 669-677, 2025.1088-68260002-9939https://hdl.handle.net/11449/30142610.1090/proc/171162-s2.0-85213802538Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengProceedings of the American Mathematical Societyinfo:eu-repo/semantics/openAccess2025-04-30T13:42:38Zoai:repositorio.unesp.br:11449/301426Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462025-04-30T13:42:38Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv A NOTE ON HILBERT 16TH PROBLEM
title A NOTE ON HILBERT 16TH PROBLEM
spellingShingle A NOTE ON HILBERT 16TH PROBLEM
Gasull, Armengol
Hilbert 16th problem
limit cycles
structurally stable vector fields
title_short A NOTE ON HILBERT 16TH PROBLEM
title_full A NOTE ON HILBERT 16TH PROBLEM
title_fullStr A NOTE ON HILBERT 16TH PROBLEM
title_full_unstemmed A NOTE ON HILBERT 16TH PROBLEM
title_sort A NOTE ON HILBERT 16TH PROBLEM
author Gasull, Armengol
author_facet Gasull, Armengol
Santana, Paulo [UNESP]
author_role author
author2 Santana, Paulo [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universitat Autònoma de Barcelona
Edifici Cc
Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Gasull, Armengol
Santana, Paulo [UNESP]
dc.subject.por.fl_str_mv Hilbert 16th problem
limit cycles
structurally stable vector fields
topic Hilbert 16th problem
limit cycles
structurally stable vector fields
description Let H(n) be the maximum number of limit cycles that a planar polynomial vector field of degree n can have. In this paper we prove that H(n) is realizable by structurally stable vector fields with only hyperbolic limit cycles and that it is a strictly increasing function whenever it is finite.
publishDate 2025
dc.date.none.fl_str_mv 2025-04-29T18:58:10Z
2025-02-01
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/10.1090/proc/17116
Proceedings of the American Mathematical Society, v. 153, n. 2, p. 669-677, 2025.
1088-6826
0002-9939
https://hdl.handle.net/11449/301426
10.1090/proc/17116
2-s2.0-85213802538
url http://dx.doi.org/10.1090/proc/17116
https://hdl.handle.net/11449/301426
identifier_str_mv Proceedings of the American Mathematical Society, v. 153, n. 2, p. 669-677, 2025.
1088-6826
0002-9939
10.1090/proc/17116
2-s2.0-85213802538
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Proceedings of the American Mathematical Society
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 669-677
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_ 1834482554217955328

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