Global asymptotic stability for the rigid polynomial differential systems of degree three

A globally asymptotically stable differential system is a differential system having a unique equilibrium point p satisfying that all its orbits, distinct from p , tend in forward time to p . To classify the differential systems that are globally asymptotically stable in the plane is one of the classical problems of the qualitative theory of differential systems. This problem is relevant due to its applications. Here we characterize the global asymptotic stable rigid polynomial differential systems of degree three. A rigid system is a differential system having in polar coordiantes its angular velocity constant. We recall that all the global asymptotic stable polynomial differential systems of degree two already have been classified.