Polynomial slow-fast systems on the Poincaré–Lyapunov sphere

Bibliographic Details
Main Author: Perez, Otavio Henrique
Publication Date: 2024
Other Authors: Silva, Paulo Ricardo da [UNESP]
Format: Article
Language: eng
Source: Repositório Institucional da UNESP
Download full: http://dx.doi.org/10.1007/s40863-024-00441-8
https://hdl.handle.net/11449/299973
Summary: The main goal of this paper is to study compactifications of polynomial slow-fast systems. More precisely, the aim is to give conditions in order to guarantee normal hyperbolicity at infinity of the Poincaré–Lyapunov sphere for slow-fast systems defined in Rn. For the planar case, we prove a global version of the Fenichel Theorem, which assures the persistence of invariant manifolds in the whole Poincaré–Lyapunov disk. We also discuss the occurrence of non normally hyperbolic points at infinity, namely: fold, transcritical and pitchfork singularities.
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spelling Polynomial slow-fast systems on the Poincaré–Lyapunov sphereGeometric singular perturbation theoryInvariant manifoldsPoincaré compactificationPoincaré–Lyapunov compactificationPolynomial vector fieldsThe main goal of this paper is to study compactifications of polynomial slow-fast systems. More precisely, the aim is to give conditions in order to guarantee normal hyperbolicity at infinity of the Poincaré–Lyapunov sphere for slow-fast systems defined in Rn. For the planar case, we prove a global version of the Fenichel Theorem, which assures the persistence of invariant manifolds in the whole Poincaré–Lyapunov disk. We also discuss the occurrence of non normally hyperbolic points at infinity, namely: fold, transcritical and pitchfork singularities.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Agence Nationale de la RechercheInstitute of Mathematics and Computer Science University of São Paulo (USP), Avenida Trabalhador São Carlense, 400Institute of Biosciences Humanities and Exact Sciences São Paulo State University (UNESP), Rua C. Colombo, 2265Institute of Biosciences Humanities and Exact Sciences São Paulo State University (UNESP), Rua C. Colombo, 2265FAPESP: 2019/10269-3FAPESP: 2021/10198-9CAPES: 2023/02959-5CNPq: 302154/2022-1CAPES: 88881.310741/2018-01CAPES: 88887.310463/2018-00Agence Nationale de la Recherche: ANR-23-CE40-0028Universidade de São Paulo (USP)Universidade Estadual Paulista (UNESP)Perez, Otavio HenriqueSilva, Paulo Ricardo da [UNESP]2025-04-29T18:48:17Z2024-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1527-1552http://dx.doi.org/10.1007/s40863-024-00441-8Sao Paulo Journal of Mathematical Sciences, v. 18, n. 2, p. 1527-1552, 2024.2316-90281982-6907https://hdl.handle.net/11449/29997310.1007/s40863-024-00441-82-s2.0-85196720355Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengSao Paulo Journal of Mathematical Sciencesinfo:eu-repo/semantics/openAccess2025-04-30T13:42:10Zoai:repositorio.unesp.br:11449/299973Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462025-04-30T13:42:10Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Polynomial slow-fast systems on the Poincaré–Lyapunov sphere
title Polynomial slow-fast systems on the Poincaré–Lyapunov sphere
spellingShingle Polynomial slow-fast systems on the Poincaré–Lyapunov sphere
Perez, Otavio Henrique
Geometric singular perturbation theory
Invariant manifolds
Poincaré compactification
Poincaré–Lyapunov compactification
Polynomial vector fields
title_short Polynomial slow-fast systems on the Poincaré–Lyapunov sphere
title_full Polynomial slow-fast systems on the Poincaré–Lyapunov sphere
title_fullStr Polynomial slow-fast systems on the Poincaré–Lyapunov sphere
title_full_unstemmed Polynomial slow-fast systems on the Poincaré–Lyapunov sphere
title_sort Polynomial slow-fast systems on the Poincaré–Lyapunov sphere
author Perez, Otavio Henrique
author_facet Perez, Otavio Henrique
Silva, Paulo Ricardo da [UNESP]
author_role author
author2 Silva, Paulo Ricardo da [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidade de São Paulo (USP)
Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Perez, Otavio Henrique
Silva, Paulo Ricardo da [UNESP]
dc.subject.por.fl_str_mv Geometric singular perturbation theory
Invariant manifolds
Poincaré compactification
Poincaré–Lyapunov compactification
Polynomial vector fields
topic Geometric singular perturbation theory
Invariant manifolds
Poincaré compactification
Poincaré–Lyapunov compactification
Polynomial vector fields
description The main goal of this paper is to study compactifications of polynomial slow-fast systems. More precisely, the aim is to give conditions in order to guarantee normal hyperbolicity at infinity of the Poincaré–Lyapunov sphere for slow-fast systems defined in Rn. For the planar case, we prove a global version of the Fenichel Theorem, which assures the persistence of invariant manifolds in the whole Poincaré–Lyapunov disk. We also discuss the occurrence of non normally hyperbolic points at infinity, namely: fold, transcritical and pitchfork singularities.
publishDate 2024
dc.date.none.fl_str_mv 2024-12-01
2025-04-29T18:48:17Z
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/s40863-024-00441-8
Sao Paulo Journal of Mathematical Sciences, v. 18, n. 2, p. 1527-1552, 2024.
2316-9028
1982-6907
https://hdl.handle.net/11449/299973
10.1007/s40863-024-00441-8
2-s2.0-85196720355
url http://dx.doi.org/10.1007/s40863-024-00441-8
https://hdl.handle.net/11449/299973
identifier_str_mv Sao Paulo Journal of Mathematical Sciences, v. 18, n. 2, p. 1527-1552, 2024.
2316-9028
1982-6907
10.1007/s40863-024-00441-8
2-s2.0-85196720355
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Sao Paulo Journal of Mathematical Sciences
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 1527-1552
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_ 1834482530692104192

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