Resumen de Meromorphic Integrability of Perturbations of Quadratic Systems
Xiongkun Wang, Changjian Liu
In this article, we study the integrability of analytic perturbations of quadratic homogeneous differential system F = F2 + h.o.t. where the origin is an isolated singular point of F2. Algaba et al. [Mediterr. J. Math. 18, 8 (2021)] proved that, under the condition that F2 is polynomially integrable, the above system is analytically integrable at the origin if and only if F is orbitally equivalent to F2. Here we give a proof in a different way from Algaba et al. Furthermore, we prove that, under the condition that F2 is rationally integrable, if the parameters of F2 satisfy certain conditions, then the above system is formal meromorphically integrable at the origin if and only if F is orbitally equivalent to F2.
