On the stability of limit cycles for planar differential systems

We consider a planar differential system , , where P and Q are functions in some open set , and . Let γ be a periodic orbit of the system in . Let be a function such that where k(x,y) is a function in and . We assume that if is such that f(p)=0 and f(p)=0, then p is a singular point. We prove that , where T>0 is the period of γ. As an application, we take profit from this equality to show the hyperbolicity of the known algebraic limit cycles of quadratic systems