On the center criterion of planar quasi-homogeneous polynomial differential systems (Q1670377)

The authors characterize the centers of quasi-homogeneous planar polynomial differential systems of any natural degree \(n.\) First, they prove that the system does not admit centers if \(n\) is even, then they present sufficient and necessary conditions for the system to admit a center if \(n\) is odd. Furthermore, the authors provide a simple method to obtain such systems with center of a given order.