Remarks on 16th weak Hilbert problem for n=2

In this paper, we obtain the exact upper bound on the number of zeros of. Abelian integrals for. all quadratic polynomial one-form over closed orbits of generic quadratic Hamiltonian systems having a saddle loop and a cusp point. This result, together with the results by Horozov and Iliev (1994 Proc. Lond. Math. Soc. 69 198-224), by Gavrilov (2001 Invent. Math. 143 449-97), and by Zhang and Li (1993 Res. Rep. 33; Adv. Math. 26 445-60), gives the final answer to the weak Hilbert 16th problem for n = 2.