On the number of limit cycles surrounding a unique singular point for polynomial differential systems of arbitrary degree Original Research Article

We study the number of limit cycles that bifurcate from the periodic orbits of the center View the MathML sourceẋ=−yR(x,y), View the MathML sourceẏ=xR(x,y) where RR is a convenient polynomial of degree 2, when we perturb it inside the class of all polynomial differential systems of degree nn. We use averaging theory for computing this number. As a consequence of our study we provide the biggest number of limit cycles surrounding a unique singular point in terms of the degree of the system, known up to now.