Abstract
Consider the family of polynomial differential systems of degree 3, or simply cubic systems x' = y, y' = - x + a1x2 + a2xy + a3y2 + a4x3 + a5x2y + a6xy2 + a7y3, in the plane R2 . An equilibrium point (x0, y0) of a planar differential system is a center if there is a neighborhood U of (x0, y0) such that U\{(x0, y0)} is filled with periodic orbits. When R2\{(x0, y0)} is filled with periodic orbits, then the center is a global center. For this family of cubic systems Lloyd and Pearson characterized in Lloyd and Pearson (Comput Math Appl 60:2797-2805, 2010) when the origin of coordinates is a center. We classify which of these centers are global centers.