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. © 2006 Elsevier Inc. All rights reserved.
|Journal||Journal of Differential Equations|
|Publication status||Published - 15 Aug 2006|
- Degenerate center
- Liapunov constants
- Nilpotent center