In this paper, we prove the existence of periodic solutions of a class of Hamiltonian systems with degenerate equilibriums under small nonlinear periodic perturbations. Actually we prove that the periodic Hamiltonian systems with small perturbations can be reducible to a periodic Hamiltonian system with an equilibrium by a periodic symplectic mapping. This result is a reformulation of the result in Lu and Xu (Nonlinear Differ Equ Appl 21:361–370, 2014) in the case of Hamiltonian systems.

中文翻译：

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一类具有退化平衡的非线性周期Hamilton系统的可约性

在本文中，我们证明了在小非线性周期扰动下具有退化平衡的一类哈密顿系统的周期解的存在。实际上，我们证明了通过周期性辛映射可以将具有小扰动的周期哈密顿系统还原为具有平衡的周期哈密顿系统。对于汉密尔顿系统，此结果是对Lu和Xu中结果的重新表述（Nonlinear Differ Equ Appl 21：361-370，2014）。