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Estimation of the number of zeros of Abelian integrals of a class of quadratic reversible system. (Chinese. English summary) Zbl 1349.34106

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 \(n\geq 5\).

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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