Center-focus determination and limit cycles bifurcation for $p:q$   homogeneous weight singular point
  The quasi-homogeneous (and in general non-homogeneous) polynomial differential systems have been studied from many different points of view. In this paper, Center-focus determination and limit cycles bifurcation for $p:q$ homogeneous weight singular point are investigated. Some prosperities of Successive function and focus values are discussed, furthermore, the method of computing focal values is given. As an example, center-focus determination and limit cycle bifurcation for $2:3$ homogeneous weight singular point are studied, three or five limit cycles in the neighborhood of origin can be obtained by different perturbations. 
Tao Liu, Feng Li, Yirong Liu, Shimin Li
math.DS