We deal with non-autonomous Hamiltonian systems of one degree of freedom. For such differential systems, we compute analytically some of their periodic solutions, together with their type of stability. The tool for proving these results is the averaging theory of dynamical systems. We present some applications of these results.

中文翻译：

---

一些扰动哈密顿系统的周期解及其稳定性

我们处理一个自由度的非自治哈密顿系统。对于这样的微分系统，我们分析计算它们的一些周期解，以及它们的稳定性类型。证明这些结果的工具是动力系统的平均理论。我们介绍了这些结果的一些应用。