In this paper we study the maximal number of limit cycles for a class of piecewise smooth near-Hamiltonian systems under polynomial perturbations. Using the second order averaging method, we obtain the maximal number of limit cycles of two systems respectively. We also present an application.

中文翻译：

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分段平均系统中极限环的分叉

在本文中，我们研究了多项式摄动下的一类分段光滑近哈密顿系统的极限环的最大数目。使用二阶平均法，我们分别获得了两个系统的极限环的最大数目。我们还提出了一个申请。