Algaba Durán, AntonioGarcía García, CristóbalReyes Columé, Manuel2025-04-252025-04-252008-04Algaba, A., García, C., & Reyes, M. (2008). The center problem for a family of systems of differential equations having a nilpotent singular point. In Journal of Mathematical Analysis and Applications (Vol. 340, Issue 1, pp. 32–43). Elsevier BV. https://doi.org/10.1016/j.jmaa.2007.07.0430022-247X1096-0813 (electrónico)https://hdl.handle.net/10272/25434We 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 subfamiliesengAtribución-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nd/3.0/es/CentersNilpotent and monodromic singular pointLyapunov functionjournal article10.1016/j.jmaa.2007.07.043open access12 Matemáticas