RT Journal Article
T1 The center problem for a family of systems of differential equations having a nilpotent singular point
A1 Algaba Durán, Antonio
A1 García García, Cristóbal
A1 Reyes Columé, Manuel
AB 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
PB Elsevier
SN 0022-247X
SN 1096-0813 (electrónico)
YR 2008
FD 2008-04
LK https://hdl.handle.net/10272/25434
UL https://hdl.handle.net/10272/25434
LA eng
NO Algaba, 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.2007.07.043
NO This work has been partially supported by deMinisterio de Ciencia y Tecnología, Plan Nacional I+D+Ico-financed with FEDER funds, in the frame of the projectMTM2004-04066 and by the  Consejería de Innovación, Ciencia y Empresa dela Junta de Andalucía (FQM-276)
DS Repositorio Institucional de la Universidad de Huelva
RD 31 may 2026