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Estimation on the number of zeros of Abelian integrals of a planar Hamiltonian system. (Chinese. English summary) Zbl 1063.34027

Summary: We study the number of zeros of Abelian integrals of a planar Hamiltonian system perturbed by a polynomial of degree \(n\). We obtain that the upper bound of the number is \([\frac{3n-1}{2}]\).

MSC:

34C08 Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.)
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
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