Some lower bounds for h(n) in Hilbert's 16th problem

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

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Detail(s)

Original languageEnglish
Pages (from-to)345-360
Journal / PublicationQualitative Theory of Dynamical Systems
Volume3
Issue number2
Publication statusPublished - 2002

Abstract

For some perturbed Z2-(or Z4-)equivariant planar Hamiltonian vector field sequnces of degree n (n = 2k - 1 and n = 3 × 2k-1 - 1, k = 2, 3,...), some new lower bounds for H(n) in Hilbert's 16th problem and configurations of compound eyes of limit cycles are given, by using the bifurcation theory of planar dynamical systems and the quadruple transformation method given by Christopher and Lloyd. It gives rise to more exact results than Ref.[6].

Research Area(s)

  • Distributions of limit cycles, Hilbert's 16th problem, Perturbed planar hamiltonian systems, Second bifurcation