In this work, we present some criteria about the existence and nonexistence of both Puiseux
inverse integrating factors VV and Puiseux first integrals HH for planar analytic vector fields …

We say that a polynomial differential system x˙= P (x, y), y˙= Q (x, y) having the origin as a
singular point is Z 2-symmetric if P (− x,− y)=− P (x, y) and Q (− x,− y)=− Q (x, y). It is known …

For a given planar differential system, a classical problem is to characterize the local
qualitative properties of equilibria. Moussu in 1982 provided a necessary and sufficient …

The blow-up method proves its effectiveness to characterize the integrability of the resonant
saddles giving the necessary conditions to have formal integrability and the sufficiency …

We consider the autonomous system of differential equations of the form= P_1 (x, y)+ P_2 (x,
y), ̇ y= Q_1 (x, y)+ Q_3 (x, y), x˙= P 1 (x, y)+ P 2 (x, y), y˙= Q 1 (x, y)+ Q 3 (x, y), where P_i P i …

Recalling that at any regular point we always have a unique particular solution curve
passing through it. In this work it is constructed such particular solution curve not passing …

In this work is characterized the analytic integrability problem around a nilpotent singularity
for differential systems in the plane under generic conditions. The analytic integrability …

We consider polynomial families of real planar vector fields for which the origin is a
monodromic nilpotent singularity having minimum Andreev number. There the centers are …

This work concerns with polynomial families of real planar vector fields having a
monodromic nilpotent singularity. The families considered are those for which the centers …

This work deals with three current and relevant problems in the qualitative theory of
differential equations. The first one is the center problem on a center manifold of differential …