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 we study the narrow relation between reversibility and the center problem and
also between reversibility and the integrability problem. It is well known that an analytic …

In this paper we study the quasi-homogeneous polynomial differential systems and provide
an algorithm for obtaining all these systems with a given degree. Using this algorithm we …

This paper is devoted to the complete classification of global phase portraits of quasi-
homogeneous but non-homogeneous coprime planar polynomial differential systems of …

We characterize the nilpotent systems whose lowest degree quasi-homogeneous term is (y,
σxn) T, σ=±1, having a formal inverse integrating factor. We prove that, for n even, the …

In this work we use the normal form theory to establish an algorithm to determine if a planar
vector field is orbitally reversible. In previous works only algorithms to determine the …

We give necessary conditions for the orbital-reversibility for a class of planar dynamical
systems, based on properties of some invariant curves. From these necessary conditions we …

In the present paper we characterize the analytic integrability around the origin of a family of
degenerate differential systems. Moreover, we study the analytic integrability of some …

In this paper, we obtain necessary and sufficient conditions for the reversibility of a quasi-
homogeneous $ n $-dimensional system. As a consequence, we get necessary conditions …

In this paper, we first classify all centers of a class of quasi-homogeneous polynomial
differential systems of degree 5. Then we extend this kind of systems to a generalized …