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On the limit cycles of a Hamiltonian under Z4-equivariant quintic perturbation

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  • Wu, Yuhai
  • Tian, Lixin
  • Hu, Yingjing

Abstract

The number and distribution of limit cycles of a perturbed Z4-equivariant Hamiltonian system are studied in this paper. The existence theory and stability theory of singular close orbits are applied to study the given perturbed system. By using the small parametric perturbation skills of differential equations, we find that the perturbed Z4-equivariant system has at least 20 limit cycles. The distribution of the above 20 limit cycles is also given.

Suggested Citation

  • Wu, Yuhai & Tian, Lixin & Hu, Yingjing, 2007. "On the limit cycles of a Hamiltonian under Z4-equivariant quintic perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 298-307.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:1:p:298-307
    DOI: 10.1016/j.chaos.2006.01.120
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    References listed on IDEAS

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    1. Wang, S. & Yu, P., 2005. "Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1317-1335.
    2. Wu, Yuhai & Han, Maoan & Liu, Xuanliang, 2005. "On the study of limit cycles of a cubic polynomials system under Z4-equivariant quintic perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 999-1012.
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