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Upper bound on the number of zeros of Abelian integrals for a class of quadratic reversible systems. (Chinese. English summary) Zbl 1240.34175

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
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