Limit cycles bifurcating from planar polynomial quasi-homogeneous centers
This paper concerns the following one-parameter family of systems \[ \begin{aligned} & \dot{x}=P(x,y)+ \varepsilon \bar{P}(x,y), \\ & \dot{y}=Q(x,y)+ \varepsilon \bar{Q}(x,y), \end{aligned} \] where \(\varepsilon \neq 0\) is a sufficiently small real perturbation parameter, \(\bar{P}\) and \(\bar{Q}\) are arbitrary real polynomials of degree \(n\). By applying the first order averaging method the authors obtain an upper bound for the maximum number of limit cycles bifurcating from the periodic orbits of any planar polynomial quasi-homogeneous center of the mentioned system.
quasi-homogeneous polynomial differential equation
scientific article; zbMATH DE number 6487581