A unified proof on the weak Hilbert 16th problem for n = 2

Fengde Chen, Chengzhi Li, Jaume Llibre, Zenghua Zhang

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Abstract

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.
Original languageEnglish
Pages (from-to)309-342
JournalJournal of Differential Equations
Volume221
DOIs
Publication statusPublished - 15 Feb 2006

Keywords

  • Abelian integral
  • Centroid curve
  • Deformation argument
  • Weak Hilbert 16th problem

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    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