On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields
| Main Author: | |
|---|---|
| Publication Date: | 2024 |
| Format: | Article |
| Language: | eng |
| Source: | Repositório Institucional da UNESP |
| Download full: | http://dx.doi.org/10.1007/s40863-024-00431-w https://hdl.handle.net/11449/298905 |
Summary: | It is known that non-hyperbolic limit cycles are structurally unstable in the set of planar smooth and analytic vector fields. In the polynomial case, it is known only that limit cycles of even degree are structurally unstable. In this paper, we prove that non-hyperbolic limit cycles of odd degree are also structurally unstable in the polynomial case, if we consider Whitney’s topology. |
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On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fieldsLimit cyclesPolynomial vector fieldsStructural stabilityIt is known that non-hyperbolic limit cycles are structurally unstable in the set of planar smooth and analytic vector fields. In the polynomial case, it is known only that limit cycles of even degree are structurally unstable. In this paper, we prove that non-hyperbolic limit cycles of odd degree are also structurally unstable in the polynomial case, if we consider Whitney’s topology.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)IBILCE-UNESP, São PauloIBILCE-UNESP, São PauloFAPESP: 2019/10269-3FAPESP: 2021/01799-9FAPESP: 2022/14353-1Universidade Estadual Paulista (UNESP)Santana, Paulo [UNESP]2025-04-29T18:40:47Z2024-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1605-1618http://dx.doi.org/10.1007/s40863-024-00431-wSao Paulo Journal of Mathematical Sciences, v. 18, n. 2, p. 1605-1618, 2024.2316-90281982-6907https://hdl.handle.net/11449/29890510.1007/s40863-024-00431-w2-s2.0-85193688718Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengSao Paulo Journal of Mathematical Sciencesinfo:eu-repo/semantics/openAccess2025-04-30T14:23:35Zoai:repositorio.unesp.br:11449/298905Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462025-04-30T14:23:35Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
| dc.title.none.fl_str_mv |
On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields |
| title |
On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields |
| spellingShingle |
On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields Santana, Paulo [UNESP] Limit cycles Polynomial vector fields Structural stability |
| title_short |
On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields |
| title_full |
On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields |
| title_fullStr |
On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields |
| title_full_unstemmed |
On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields |
| title_sort |
On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields |
| author |
Santana, Paulo [UNESP] |
| author_facet |
Santana, Paulo [UNESP] |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (UNESP) |
| dc.contributor.author.fl_str_mv |
Santana, Paulo [UNESP] |
| dc.subject.por.fl_str_mv |
Limit cycles Polynomial vector fields Structural stability |
| topic |
Limit cycles Polynomial vector fields Structural stability |
| description |
It is known that non-hyperbolic limit cycles are structurally unstable in the set of planar smooth and analytic vector fields. In the polynomial case, it is known only that limit cycles of even degree are structurally unstable. In this paper, we prove that non-hyperbolic limit cycles of odd degree are also structurally unstable in the polynomial case, if we consider Whitney’s topology. |
| publishDate |
2024 |
| dc.date.none.fl_str_mv |
2024-12-01 2025-04-29T18:40:47Z |
| 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/s40863-024-00431-w Sao Paulo Journal of Mathematical Sciences, v. 18, n. 2, p. 1605-1618, 2024. 2316-9028 1982-6907 https://hdl.handle.net/11449/298905 10.1007/s40863-024-00431-w 2-s2.0-85193688718 |
| url |
http://dx.doi.org/10.1007/s40863-024-00431-w https://hdl.handle.net/11449/298905 |
| identifier_str_mv |
Sao Paulo Journal of Mathematical Sciences, v. 18, n. 2, p. 1605-1618, 2024. 2316-9028 1982-6907 10.1007/s40863-024-00431-w 2-s2.0-85193688718 |
| dc.language.iso.fl_str_mv |
eng |
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eng |
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Sao Paulo Journal of Mathematical Sciences |
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info:eu-repo/semantics/openAccess |
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openAccess |
| dc.format.none.fl_str_mv |
1605-1618 |
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Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
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Universidade Estadual Paulista (UNESP) |
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UNESP |
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UNESP |
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Repositório Institucional da UNESP |
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Repositório Institucional da UNESP |
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Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
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repositoriounesp@unesp.br |
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1834482397292265472 |