The center problem for the class of Λ- Ω differential systems
The center problem, i.e. distinguish between a focus and a center, is a classical problem in the qualitative theory of planar differential equations which go back to Darboux, Poincaré and Liapunov. Here we solve the center problem for the class of planar analytic or polynomial differential systems x...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:239784 |
| Acceso en línea: | https://ddd.uab.cat/record/239784 https://dx.doi.org/urn:doi:10.1007/s12215-020-00568-5 |
| Access Level: | acceso abierto |
| Palabra clave: | First integral Poincaré-Liapunov first integral Analytic planar differential system Polynomial differential system Weak center |
| Sumario: | The center problem, i.e. distinguish between a focus and a center, is a classical problem in the qualitative theory of planar differential equations which go back to Darboux, Poincaré and Liapunov. Here we solve the center problem for the class of planar analytic or polynomial differential systems x˙= -y + X = -y + ∑j=2k Xj, y˙= x + Y = x + ∑j=2k Yj, k≤∞, where Xj = Xj(x,y)and Yj = Yj(x,y) are homogenous polynomials of degree j. |
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