In this work we deal with analytic families of real planar vector fields $\mathcal {X} _\lambda
$ having a monodromic singularity at the origin for any $\lambda\in\Lambda\subset\mathbb …

We analyze the structure of the Poincar\'e map $\Pi $ associated to a monodromic singularity
of an analytic family of planar vector fields. We work under two assumptions. The first one is …

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 …

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 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 …

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 …

In this work, we analyze some aspects of the center problem from the perspective of the
normal form theory. We provide alternative proofs of some well known results in the case of …

In this work we focus in the family of real planar polynomial vector fields of arbitrary degree.
We are interested in to characterize when a (local) center singularity of these vector fields …

This paper aims to provide sufficient and necessary conditions for the monodromic problem
and center problem of continuous piecewise linear systems with arbitrary finite number of …

In this paper, we use a geometric criterium based on the classical method of the construction
of Lyapunov functions to determine if a differential system has a focus or a center at a …