Bifurcation of limit cycles and center problem for \(p : q\) homogeneous weight systems (Q1729228)

In this paper, the authors consider quasi-homogeneous polynomial differential systems and study the center problem and bifurcation of limit cycles for $p:q$ homogeneous weight systems. Some properties of the successive function and the focus values are discussed. Furthermore, the method of computing focal values is given. As an example, the center problem and the bifurcation of limit cycles for a $2:3$ homogeneous weight system are studied, three or five limit cycles in the neighborhood of the origin can be obtained by different perturbations.