Song, Yan Estimation on the number of zeros of Abelian integrals of a planar Hamiltonian system. (Chinese. English summary) Zbl 1063.34027 J. Math. Res. Expo. 23, No. 4, 651-657 (2003). Summary: We study the number of zeros of Abelian integrals of a planar Hamiltonian system perturbed by a polynomial of degree \(n\). We obtain that the upper bound of the number is \([\frac{3n-1}{2}]\). MSC: 34C08 Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) 37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems Keywords:Picard-Fuchs equation PDFBibTeX XMLCite \textit{Y. Song}, J. Math. Res. Expo. 23, No. 4, 651--657 (2003; Zbl 1063.34027)