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 …

In this paper, bi-center problem and bifurcation of limit cycles from nilpotent singular points
in Z 2-equivariant cubic vector fields are studied. First, the system is simplified by using …

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 …

The aim of this work is to give conditions on the parameters of a family of analytic planar
vector fields with a fixed Newton diagram and a monodromic singularity in order to …

The relation between limit cycles of planar differential systems and the inverse integrating
factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From …

Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields -
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We prove that all the nilpotent centers of planar analytic differential systems are limit of
centers with purely imaginary eigenvalues, and consequently the Poincaré–Liapunov …

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 paper we determine the centers of quasi-homogeneous polynomial planar vector
fields of degree 0, 1, 2, 3 and 4. In addition, in every case we make a study of the reversibility …

In this work, a new perturbation approach is developed based on Bogdanov-Takens
bifurcation theory, which enables the Poincaré-Lyapunov method for switching systems with …