Quartic rigid systems in the plane and in the Poincaré sphere

M. J. Álvarez, J. L. Bravo, L. A. Calderón

We consider the planar family of rigid systems of the form $x^{\prime }=-y+xP(x,y),y^{\prime }=x+yP(x,y)$, where $P$ is any polynomial with monomials of degree one and three. This is the simplest n…