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 prove that all the nilpotent centers of planar analytic differential systems are limit of
centers with purely imaginary eigenvalues, and consequently the Poincaré–Liapunov …

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 …

To characterize when a nilpotent singular point of an analytic differential system is a center
is of particular interest, first for the problem of distinguishing between a focus and a center …

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 paper, bifurcation of limit cycles is considered for planar cubic-order systems with an
isolated nilpotent critical point. Normal form theory is applied to compute the generalized …

Characterization of a monodromic singular point of a planar vector field - ScienceDirect Skip to
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In this paper, we are interested in the nilpotent centre problem of planar analytic
monodromic vector fields. It is known that the formal integrability is not enough to …

This work is focused in the center problem for nilpotent singularities of differential systems in
the plane. Although there are involved methods to approach the center problem in this work …

We give an expression of the irreducible invariant curves at the singular point. For
analytically integrable systems, we provide an expression of its primitive first integral. This …