The hyperelliptic limit cycles of the Liénard systems

For Liénard systems x˙=y, y˙=−fm(x)y−gn(x) with fm and gn real polynomials of degree m and n respectively, in [H. Zoladek, Algebraic invariant curves for the Liénard equation, Trans. Amer. Math. Soc. 350 (1998) 1681-1701] the author showed that if m⩾3 and m+14 and m+1