The blow up technique is widely used in desingularization of degenerate singular points of
planar vector fields. In this survey, we give an overview of the different types of blow up and …

In this paper we consider perturbations of quasi-homogeneous planar Hamiltonian systems,
where the Hamiltonian function does not contain multiple factors. It is important to note that …

In this work we study the centers of planar analytic vector fields which are limit of linear type
centers. It is proved that all the nilpotent centers are limit of linear type centers and …

We give a new and short proof of the characterization of monodromic nilpotent critical points.
We also calculate the first generalized Lyapunov constants in order to solve the stability …

We consider the two-dimensional autonomous systems of differential equations where the
origin is a monodromic degenerate singular point, ie, with null linear part. In this work we …

Consider the two-dimensional autonomous systems of differential equations of the form...= P
[sub 3](x, y)+ P [sub 4](x, y),...=(Q [sub 3](x, y)+ Q [sub 4](x, y), where P [sub 3](x, y) and Q …

This paper deals with planar quasi-homogeneous polynomial vector fields, and addresses
three major questions: the monodromy, the center–focus and the integrability problems. We …

We consider analytic families of planar vector fields depending analytically on the
parameters in Λ that guarantee the existence of a (may be degenerate and with …

In this work we continue the study of the centers which are limits of linear type centers. It is
proved that if a degenerate center has an inverse integrating factor V (x, y) with V (0, 0)≠ 0 …

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 …