The weak Hilbert 16th problem for n = 2 was solved by Horozov and Iliev (Proc. London Math. Soc. 69 (1994) 198-244), Zhang and Li (Adv. in Math. 26 (1997) 445-460), (Gavrilov Invent. Math. 143 (2001) 449-497), and Li and Zhang (Nonlinearity 15 (2002) 1775-1992), by using different methods for different cases. The aim of this paper is to give a unified and easier proof for all cases. The proof is restricted to the real domain, combines geometric and analytical methods, and uses deformation arguments. © 2005 Elsevier Inc. All rights reserved.
|Journal||Journal of Differential Equations|
|Publication status||Published - 15 Feb 2006|
- Abelian integral
- Centroid curve
- Deformation argument
- Weak Hilbert 16th problem
Chen, F., Li, C., Llibre, J., & Zhang, Z. (2006). A unified proof on the weak Hilbert 16th problem for n = 2. Journal of Differential Equations, 221, 309-342. https://doi.org/10.1016/j.jde.2005.01.009