Hong, Xiaochun; Ma, Rui; Wang, Bin Estimation of the number of zeros of Abelian integrals of a class of quadratic reversible system. (Chinese. English summary) Zbl 1349.34106 Math. Pract. Theory 45, No. 5, 270-276 (2015). Summary: By using the method of Picard-Fuchs equation and the Riccati equation method, we give an estimation of the number of zeros of abelian integrals of a class of quadratic reversible system under polynomial perturbations of arbitrary degree \(n\). The upper bound is \(10\left[\frac{4n+1}{3}\right] + 4\left[\frac{4n}{3}\right] + \left[\frac{4n-1}{3}\right] + 13\) when \(n\geq 5\). Cited in 1 Document MSC: 34C08 Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) 34C14 Symmetries, invariants of ordinary differential equations Keywords:quadratic reversible system; abelian integral; Picard-Fuchs equation; Riccati equation PDFBibTeX XMLCite \textit{X. Hong} et al., Math. Pract. Theory 45, No. 5, 270--276 (2015; Zbl 1349.34106)