A codimension-three Takens–Bogdanov bifurcation in reversible systems has been very
recently analyzed in the literature. In this paper, we study with the help of the nonlinear time …

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 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 …

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 …

In this paper, we study the Lotka–Volterra complex cubic systems. We obtain necessary
conditions of integrability for these systems with some restriction on the parameters. The …

We consider the autonomous system of differential equations of the form= P_1 (x, y)+ P_2 (x,
y), ̇ y= Q_1 (x, y)+ Q_3 (x, y), x˙= P 1 (x, y)+ P 2 (x, y), y˙= Q 1 (x, y)+ Q 3 (x, y), where P_i P i …

In this paper, we consider the orbital-reversibility problem for an n-dimensional vector field,
which consists in determining if there exists a time-reparametrization that transforms the …

We consider a class of three-dimensional systems having an equilibrium point at the origin,
whose principal part is of the form (−∂ h∂ y (x, y),∂ h∂ x (x, y), f (x, y)) T. This principal …

We prove that for every planar differential system with a period annulus there exists a unique
involution σ σ such that the system is σ σ-symmetric. We also prove that, given a system with …

In this work we study the center conditions of a particular polynomial differential system with
a nilpotent singularity using a new proposed algorithm. This problem was initially studied in …