@article{10272/25434,
year = {2008},
month = {4},
url = {https://hdl.handle.net/10272/25434},
abstract = {We study the analytic system of differential equations in the plane(over(x, ̇), over(y, ̇))t = underover(∑, i = 0, ∞) Fq - p + 2 i s, 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 + 2 s (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},
organization = {This work has been partially supported by de
Ministerio de Ciencia y Tecnología, Plan Nacional I+D+I
co-financed with FEDER funds, in the frame of the project
MTM2004-04066 and by the  Consejería de Innovación, Ciencia y Empresa de
la Junta de Andalucía (FQM-276)},
publisher = {Elsevier},
title = {The center problem for a family of systems of differential equations having a nilpotent singular point},
doi = {10.1016/j.jmaa.2007.07.043},
author = {Algaba Durán, Antonio and García García, Cristóbal and Reyes Columé, Manuel},
}