On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914803453263872 |
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| author | Santana, Paulo |
| author_facet | Santana, Paulo |
| contents | It is known that non-hyperbolic limit cycles are structurally unstable in the set of planar smooth and analytical 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_00220 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields Santana, Paulo Dynamical Systems It is known that non-hyperbolic limit cycles are structurally unstable in the set of planar smooth and analytical 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. |
| title | On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2303.00220 |