In this work, we are interested in isolated crossing periodic orbits in planar piecewise polynomial vector fields defined in two zones separated by a straight line. In particular, in the number of limit cycles of small ...

Let N = {y > 0} and S = {y < 0} be the semi-planes of R-2 having as common boundary the line D = {y = 0}. Let X and Y be polynomial vector fields defined in N and S, respectively, leading to a discontinuous piecewise ...

The main goal of this paper is to present the behavior generated by piecewise smooth vector fields tangent to foliations. We consider two smooth foliations F1 and F2 that are coupled to produce a foliation composed by ...

The main goal of this paper is to exhibit normal forms of generic locally structurally stable piecewise smooth vector fields on R-3. Besides, we construct the homeomorphism that gives the topological equivalence between ...

In this paper, we are dealing with piecewise smooth vector fields in a 2D-manifold. In such a scenario, the main goal of this paper is to exhibit the homeomorphism that gives the topological equivalence between a codimension ...

In this work we study the dynamics at infinity of a piecewise smooth vector fields in ℝ3. We provide conditions for the 24-parameter family to undergo a local bifurcations of codimension zero and one at infinity. These ...

When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x˙=−y((x2+y2)/2)m and y˙=x((x2+y2)/2)m with m≥1, when we ...

We study the stability of an invisible fold-fold singularity of planar piecewise smooth Hamiltonian vector fields by computing some kind of Lyapunov coefficients. We obtain the general expressions for the first five Lyapunov ...