Quartic Rigid Systems in the Plane and in the Poincaré Sphere

Abstract

[eng] We consider the planar family of rigid systems of the form x′ = −y + x P(x, y), y′ = x + y P(x, y), where P is any polynomial with monomials of degree one and three. This is the simplest non-trivial family of rigid systems with no rotatory parameters. The family can be compactified to the Poincaré sphere such that the vector field along the equator is not identically null . We study the centers, singular points and limit cycles of that family on the plane and on the sphere.