On the Paper of Jin and Wang Concerning the conditions for a Centre in certain Cubic Systems

In a preceding paper of Jin and Wang the authors describe computations concerning differential systems of the form x=y, y=-x+a 1 x 2 +a 2 xy+a 3 y 2 +a 4 x x3 +a 5 x 2 y+a 6 xy 2 +a 7 y 3 . We give proofs of the results suggested by these computations and provide a full description of the bifurcation of small-amplitude limit cycles in a subclass of these systemes