The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
In this work we study the centers of planar analytic vector fields which are limit of linear type centers. It is proved that all the nilpotent centers are limit of linear type centers and consequently the Poincaré–Liapunov method to find linear type centers can be also used to find the nilpotent cen...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2006 |
| País: | España |
| Institución: | Universitat de Lleida (UdL) |
| Repositorio: | Repositori Obert UdL |
| OAI Identifier: | oai:repositori.udl.cat:10459.1/57797 |
| Acceso en línea: | https://doi.org/10.1016/j.jde.2006.03.012 http://hdl.handle.net/10459.1/57797 |
| Access Level: | acceso abierto |
| Palabra clave: | Nilpotent center Degenerate center Liapunov constants Cyclicity Equacions diferencials |
| Sumario: | In this work we study the centers of planar analytic vector fields which are limit of linear type centers. It is proved that all the nilpotent centers are limit of linear type centers and consequently the Poincaré–Liapunov method to find linear type centers can be also used to find the nilpotent centers. Moreover, we show that the degenerate centers which are limit of linear type centers are also detectable with the Poincaré–Liapunov method. |
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