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 centers. Moreover, we show that the degenerate centers which are limit of linear type centers are also detectable with the Poincaré-Liapunov method.     

On the analytic solvability of the problem of distinguishing between center and focus

The analytic solvability of the problem of distinguishing between a center and a focus is proved in each of semialgebraic subsets whose union is the entire set of monodromic germs.     

Corrigendum to “Complex contact Lie groups and generalized complex Heisenberg groups” [Differential Geom. Appl. 24 (2006) 443-446]

We restate and prove the main theorem of the paper “Complex contact Lie groups and generalized complex Heisenberg groups”.