Nine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent center
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摘要
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.
论文关键词:Near-Hamiltonian system,Nilpotent center,Hopf bifurcation,Limit cycle,Normal form,Generalized Lyapunov constant
论文评审过程:Received 2 May 2015, Revised 14 August 2016, Accepted 14 November 2016, Available online 28 November 2016, Version of Record 28 November 2016.
论文官网地址:https://doi.org/10.1016/j.amc.2016.11.021