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Nine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent center

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  • Yang, Junmin
  • Yu, Pei

Abstract

In this paper, we study bifurcation of limit cycles in planar cubic near-Hamiltonian systems with a nilpotent center. We use normal form theory to compute the generalized Lyapunov constants and show that there exist at least 9 limit cycles around the nilpotent center. This is a new lower bound on the number of limit cycles in planar cubic near-Hamiltonian systems with a nilpotent center.

Suggested Citation

  • Yang, Junmin & Yu, Pei, 2017. "Nine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent center," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 141-152.
    • Handle: RePEc:eee:apmaco:v:298:y:2017:i:c:p:141-152
    DOI: 10.1016/j.amc.2016.11.021
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    References listed on IDEAS

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    1. Yu, P. & Han, M., 2005. "Small limit cycles bifurcating from fine focus points in cubic order Z2-equivariant vector fields," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 329-348.
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