The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems

Details The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems

2005-06-07

arxiv.org/abs/math/0506116v2

Mathematics

Dynamical Systems

24 pages, no figures

Scientific paper

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 Poincar\'e--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 Poincar\'e--Liapunov method.

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