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Zeros of abelian integral for a kind of Hamiltonian systems. (Chinese. English summary) Zbl 1449.34111

Summary: In this paper, we obtain an upper bound for the number of zeros of the Abelian integral for a class of Hamiltonian systems. The abelian integral has \(k + 2\) generators which satisfy two different Picard-Fuchs equations. Finally, we present two examples to illustrate an application of the theoretical result.

MSC:

34C08 Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.)
34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations
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