Bifurcations of limit cycles in a Z6-equivariant planar vector field of degree 5

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Original languageEnglish
Pages (from-to)817-826
Journal / PublicationScience in China, Series A: Mathematics
Issue number7
Publication statusPublished - Jul 2002


A concrete numerical example of Z6-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcation theory of planar dynamical systems and the method of detection functions. There is reason to conjecture that the Hilbert number H(2k + 1) ≥ (2k + 1)2 - 1 for the perturbed Hamiltonian systems.

Research Area(s)

  • Equivariant vector field, Hilbert's 16th problem, Limit cycle, Method of detection function, Polynomial system