Consider the family of polynomial differential systems of degree 3, or simply cubic systems x ' = y , y ' = - x + a 1 x 2 + a 2 x y + a 3 y 2 + a 4 x 3 + a 5 x 2 y + a 6 x y 2 + a 7 y 3 , in the plane R 2 . An equilibrium point ( x 0 , y 0 ) of a planar differential system is a center if there is a neighborhood U of ( x 0 , y 0 ) such that U \ { ( x 0 , y 0 ) } is filled with periodic orbits. When R 2 \ { ( x 0 , y 0 ) } 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.
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