Abstract

The weak Hibert´s 16th problem for n=2 was solved by Horozov and Iliev (1994 Proc. London Math Soc. 69:198-244), Zhang and Li (1997 Adv.Math. 26:445-460), Gavrilov (2001 Invent. Math. 143:449-497), and Li and Zhang (2002 Nonlinearity 15:1775-1992), by using different methods for different cases. The aim of a recent preprint with F.Cheng, J.Llibre and Z.Zhang is to give a uniform and easier proof for all cases. I will give a brief introduction about this problem, the relative results, and the basic idea in our uniform proof.