Hong, Xiaochun Upper bound on the number of zeros of Abelian integrals for a class of quadratic reversible systems. (Chinese. English summary) Zbl 1240.34175 Acta Math. Appl. Sin. 33, No. 5, 769-779 (2010). Summary: By using the method of Picard-Fuchs equation and the Riccati equation method, we give a linear estimate of the number of zeros of Abelian integrals for quadratic reversible systems under polynomial perturbations of arbitrary degree \(n\). The upper bound is \(4\big[\frac{2n}3\big]+2\big[\frac{2n+1}3\big]+\big[\frac{2n+2}3\big]+16\) for \(n\geq 3\). 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}, Acta Math. Appl. Sin. 33, No. 5, 769--779 (2010; Zbl 1240.34175)