On a variant of Hilbert's 16th problem
We study the number of limit cycles that a planar polynomial vector field can have as a function of its number m of monomials. We prove that the number of limit cycles increases at least quadratically with m and we provide good lower bounds for m ≤ 10.
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:307723 |
| Acceso en línea: | https://ddd.uab.cat/record/307723 https://dx.doi.org/urn:doi:10.1088/1361-6544/ad8c1b |
| Access Level: | acceso abierto |
| Palabra clave: | Limit cycles Hilbert 16th problem Abelian integrals |
| Sumario: | We study the number of limit cycles that a planar polynomial vector field can have as a function of its number m of monomials. We prove that the number of limit cycles increases at least quadratically with m and we provide good lower bounds for m ≤ 10. |
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