Algebraic limit cycles on quadratic polynomial differential systems
Algebraic limit cycles in quadratic polynomial differential systems started to be studied in 1958, and few years later the following conjecture appeared: Quadratic polynomial differential systems have at most one algebraic limit cycle. We prove that for a quadratic polynomial differential system hav...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:199354 |
| Acceso en línea: | https://ddd.uab.cat/record/199354 https://dx.doi.org/urn:doi:10.1017/S0013091517000244 |
| Access Level: | acceso abierto |
| Palabra clave: | Algebraic limit cycles Quadratic polynomial differential system Quadratic polynomial vector field |
| Sumario: | Algebraic limit cycles in quadratic polynomial differential systems started to be studied in 1958, and few years later the following conjecture appeared: Quadratic polynomial differential systems have at most one algebraic limit cycle. We prove that for a quadratic polynomial differential system having an invariant algebraic curve with at most one pair of diametrally opposite singular point at infinity, has at most one algebraic limit cycle. Our result provides a partial positive answer to this conjecture. |
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