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The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems |
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| Authors: | Hector Giacomini Jaume Llibre |
| Affiliation: | a Laboratoire de Mathématique et Physique Théorique, CNRS (UMR 6083), Faculté des Sciences et Techniques, Université de Tours, Parc de Grandmont, 37200 Tours, France b Departament de Matemàtica, Universitat de Lleida, Av. Jaume II, 69. 25001 Lleida, Spain c Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain |
| Abstract: | 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. |
| Keywords: | primary, 34C05 secondary, 58F14 |
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