On the number of limit cycles in near-hamiltonian polynomial systems

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)2033-2047
Journal / PublicationInternational Journal of Bifurcation and Chaos
Issue number6
Publication statusPublished - Jun 2007


In this paper we study a general near-Hamiltonian polynomial system on the plane. We suppose the unperturbed system has a family of periodic orbits surrounding a center point and obtain some sufficient conditions to find the cyclicity of the perturbed system at the center or a periodic orbit. In particular, we prove that for almost all polynomial Hamiltonian systems the perturbed systems with polynomial perturbations of degree n have at most n(n + l)/2 -1 limit cycles near a center point. We also obtain some new results for Lienard systems by applying our main theorems. © World Scientific Publishing Company.

Research Area(s)

  • Bifurcation, Cyclicity, Limit cycle, Near-Hamiltonian system