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Polynomial systems: a lower bound for the weakened 16th Hilbert problem.

Chengzhi Li; Weigu Li; Jaume Llibre; Zhifen Zhang — 2001

Extracta Mathematicae

In this paper we provide the greatest lower bound about the number of (non-infinitesimal) limit cycles surrounding a unique singular point for a planar polynomial differential system of arbitrary degree.

Abelian integrals of quadratic Hamiltonian vector fields with an invariant straight line.

Chengzhi Li; Jaume Llibre; Zhi-fen Zhang — 1995

Publicacions Matemàtiques

We prove that the lowest upper bound for the number of isolated zeros of the Abelian integrals associated to quadratic Hamiltonian vector fields having a center and an invariant straight line after quadratic perturbations is one.

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