SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 1343-1371, January 2020.
We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed system presents a simple twofold cycle, which is characterized by a closed trajectory connecting a visible twofold singularity to itself. It is shown that under certain generic conditions the perturbed system has sliding and crossing periodic solutions. In order to get our results, Melnikov's ideas are applied together with tools from the geometric singular perturbation theory. Finally, a study of a perturbed piecewise Hamiltonian model is performed.

中文翻译：

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具有双重周期的平面可逆Filippov系统周期摄动的周期轨道研究

SIAM应用动力系统杂志，第19卷，第2期，第1343-1371页，2020年1月。
我们研究了一类平面Filippov系统中周期解的存在，该系统是由可逆分段光滑微分系统的非自治周期扰动获得的。假定不受干扰的系统呈现出一个简单的双重循环，其特征是闭合的轨迹将其自身连接了一个可见的双重奇点。结果表明，在某些一般条件下，扰动系统具有滑动和交叉周期解。为了获得我们的结果，将梅尔尼科夫的思想与几何奇异摄动理论的工具一起应用。最后，对摄动的分段哈密顿量模型进行了研究。