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

Tomas Johnson; Warwick Tucker

doi:10.1142/S0218127410026599

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

Tomas Johnson, Warwick Tucker

Research output: Contribution to journal › Article › Research › peer-review

8 Citations (Scopus)

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 language	English
Pages (from-to)	1451-1458
Number of pages	8
Journal	International Journal of Bifurcation and Chaos
Volume	20
Issue number	5
DOIs	https://doi.org/10.1142/S0218127410026599
Publication status	Published - May 2010
Externally published	Yes

Keywords

Abelian integrals
bifurcation theory
interval analysis
limit cycles
planar Hamiltonian systems

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10.1142/S0218127410026599

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AB - 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.

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KW - bifurcation theory

KW - interval analysis

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KW - planar Hamiltonian systems

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

Abstract

Keywords

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