An improved lower bound on the number of limit cycles bifurcating from a hamiltonian planar vector field of degree 7

Tomas Johnson, Warwick Tucker

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Abstract

The limit cycle bifurcations of a Z2 equivariant planar Hamiltonian vector field of degree 7 under Z2 equivariant degree 7 perturbation is studied. We prove that the given system can have at least 53 limit cycles. This is an improved lower bound for the weak formulation of Hilbert's 16th problem for degree 7, i.e. on the possible number of limit cycles that can bifurcate from a degree 7 planar Hamiltonian system under degree 7 perturbation.

Original languageEnglish
Pages (from-to)1451-1458
Number of pages8
JournalInternational Journal of Bifurcation and Chaos
Volume20
Issue number5
DOIs
Publication statusPublished - May 2010
Externally publishedYes

Keywords

  • Abelian integrals
  • bifurcation theory
  • interval analysis
  • limit cycles
  • planar Hamiltonian systems

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