The aim of this paper is the study of the center-focus and cyclicity problems inside the class X of 3-dimensional vector fields that admit a first integral that leaves invariant any sphere centered at the origin. We classify ...

The aim of this paper is the study of the center-focus and cyclicity problems inside the class X of 3-dimensional vector fields that admit a first integral that leaves invariant any sphere centered at the origin. We classify ...

Invariant algebraic surfaces are commonly observed in differential systems arising in mathematical modeling of natural phenomena. In this paper, we study the integrability and dynamics of quadratic polynomial differential ...

From the normal form of polynomial differential systems in R3 having a sphere as invariant algebraic surface, we obtain a class of quadratic systems depending on ten real parameters, which encompasses the well-known Sprott ...

We search for invariant solutions of the conformal Killing–Yano equation on Lie groups equipped with left invariant Riemannian metrics, focusing on 2-forms. We show that when the Lie group is compact equipped with a ...

We consider the well-known Sprott A system, which depends on a single real parameter a and, for a= 1 , was shown to present a hidden chaotic attractor. We study the formation of hidden chaotic attractors as well as the ...

We search for invariant solutions of the conformal Killing-Yano equation on Lie groups equipped with left invariant Riemannian metrics, focusing on 2-forms. We show that when the Lie group is compact equipped with a ...

In this paper by using the Poincare compactification of R(3) we describe the global dynamics of the Lorenz system(x) over dot = s(-x + y), (y) over dot = rx - y - xz, (z) over dot = -bz + xy,having some invariant algebraic ...

In this paper by using the Poincare compactification of R(3) we describe the global dynamics of the Lorenz system(x) over dot = s(-x + y), (y) over dot = rx - y - xz, (z) over dot = -bz + xy,having some invariant algebraic ...