An improved lower bound on the number of limit cycles bifurcating from a quintic hamiltonian planar vector field under quintic perturbation

Tomas Johnson; Warwick Tucker

doi:10.1142/S0218127410025405

An improved lower bound on the number of limit cycles bifurcating from a quintic hamiltonian planar vector field under quintic perturbation

Tomas Johnson, Warwick Tucker

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

4 Citations (Scopus)

Abstract

The limit cycle bifurcation of a Z₂ equivariant quintic planar Hamiltonian vector field under Z₂ equivariant quintic perturbation is studied. We prove that the given system can have at least 27 limit cycles. This is an improved lower bound on the possible number of limit cycles that can bifurcate from a quintic planar Hamiltonian system under quintic perturbation.

Original language	English
Pages (from-to)	63-70
Number of pages	8
Journal	International Journal of Bifurcation and Chaos
Volume	20
Issue number	1
DOIs	https://doi.org/10.1142/S0218127410025405
Publication status	Published - Jan 2010
Externally published	Yes

Keywords

Bifurcation theory
Interval analysis
Limit cycles
Planar Hamiltonian systems

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10.1142/S0218127410025405

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title = "An improved lower bound on the number of limit cycles bifurcating from a quintic hamiltonian planar vector field under quintic perturbation",

abstract = "The limit cycle bifurcation of a Z2 equivariant quintic planar Hamiltonian vector field under Z2 equivariant quintic perturbation is studied. We prove that the given system can have at least 27 limit cycles. This is an improved lower bound on the possible number of limit cycles that can bifurcate from a quintic planar Hamiltonian system under quintic perturbation.",

keywords = "Bifurcation theory, Interval analysis, Limit cycles, Planar Hamiltonian systems",

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AU - Tucker, Warwick

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N2 - The limit cycle bifurcation of a Z2 equivariant quintic planar Hamiltonian vector field under Z2 equivariant quintic perturbation is studied. We prove that the given system can have at least 27 limit cycles. This is an improved lower bound on the possible number of limit cycles that can bifurcate from a quintic planar Hamiltonian system under quintic perturbation.

AB - The limit cycle bifurcation of a Z2 equivariant quintic planar Hamiltonian vector field under Z2 equivariant quintic perturbation is studied. We prove that the given system can have at least 27 limit cycles. This is an improved lower bound on the possible number of limit cycles that can bifurcate from a quintic planar Hamiltonian system under quintic perturbation.

KW - Bifurcation theory

KW - Interval analysis

KW - Limit cycles

KW - Planar Hamiltonian systems

UR - https://www.scopus.com/pages/publications/77951557844

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JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

IS - 1

ER -

An improved lower bound on the number of limit cycles bifurcating from a quintic hamiltonian planar vector field under quintic perturbation

Abstract

Keywords

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