Bai, Long; Yang, Jihua Linear estimate for the number of zeros of abelian integrals of Hamiltonian system with singular line. (Chinese. English summary) Zbl 1389.34103 J. Northwest Norm. Univ., Nat. Sci. 53, No. 2, 13-16, 20 (2017). Summary: It is proved that the number of zeros of abelian integral for the Hamiltonian system \[ \dot x=xy(2+2x-3y),\, \dot y =-y^2(1+2x-y) \] with singular line under perturbations of polynomials with degree \(n\) is not more than \(7\left[\frac{n}{4}\right]+8\) (taking into account the multiplicity). MSC: 34C08 Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010) Keywords:singular line; Hamiltonian system; abelian integral; Picard-Fuchs equation PDFBibTeX XMLCite \textit{L. Bai} and \textit{J. Yang}, J. Northwest Norm. Univ., Nat. Sci. 53, No. 2, 13--16, 20 (2017; Zbl 1389.34103) Full Text: DOI