A note on Hilbert 16th problem
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.
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:309367 |
| Acceso en línea: | https://ddd.uab.cat/record/309367 https://dx.doi.org/urn:doi:10.1090/proc/17116 |
| Access Level: | acceso abierto |
| Palabra clave: | Hilbert 16th problem Limit cycles Structurally stable vector fields |
| Sumario: | 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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