In this work it is characterized the analytic integrability problem around a nilpotent singularity
of a differential system in the plane under generic conditions.

We investigate the local integrability and linearizability of three dimensional Lotka–Volterra
equations at the origin. Necessary and sufficient conditions for both integrability and …

We investigate the simultaneous existence of two centers and their isochronicity for two
families of planar Z 2-equivariant differential systems. First, for a family studied by Liu and Li …

In this paper we investigate the integrability problem for the two-dimensional Lotka-Volterra
complex quartic systems which are linear systems perturbed by fourth degree homogeneous …

We provide a method to compute the necessary conditions of integrability for planar
differential systems with a weak saddle at the origin. The method is used to characterize the …

The computational problems which appear in the computation of the Poincaré–Liapunov
constants and the determination of their functionally independent number has led in recent …

In this work we provide an effective method to prove the formal integrability of the resonant
saddles. The method is based on the use of a blow-up and the resolution of a recurrence …

The center problem and the composition condition for a family of quartic differential systems
Page 1 Electronic Journal of Qualitative Theory of Differential Equations 2018, No. 15, 1–17; …

BIFURCATION OF CRITICAL PERIODS OF A QUINTIC SYSTEM 1. Introduction Consider a
system of ordinary differential equations on R2 o Page 1 Electronic Journal of Differential …

The main objective of this paper is to find necessary and sufficient conditions for a 1:− 4
resonant system of the form x˙= x− a 10 x 2− a 01 xy− a 12 y 2, y˙=− 4 y+ b 2,− 1 x 2+ b 10 x …