The center problem for a family of systems of differential equations having a nilpotent singular point
- Algaba, A.
- García, C.
- Reyes, M.
Publication date
April 2008
DOI Publisher
Elsevier Inc. ISSN
0022-247X Citation count (estimate)
21Abstract
AbstractWe study the analytic system of differential equations in the plane(x˙,y˙)t=∑i=0∞Fq−p+2is, where p,q∈N, p⩽q, s=(n+1)p−q>0, n∈N, and Fi=(Pi,Qi)t are quasi-homogeneous vector fields of type t=(p,q) and degree i, with Fq−p=(y,0)t and Qq−p+2s(1,0)<0. The origin of this system is a nilpotent and monodromic isolated singular point. We prove for this system the existence of a Lyapunov function and we solve theoretically the center problem for such system. Finally, as an application of the theoretical procedure, we characterize the centers of several subfamilies
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