We study the existence of limit cycles in planar piecewise linear Hamiltonian systems with three zones without equilibrium points. In this scenario, we have shown that such systems have at most one crossing limit cycle.

中文翻译：

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具有三个无平衡点的区域的平面分段线性哈密顿系统的极限环

我们研究了具有三个没有平衡点的区域的平面分段线性哈密顿系统中极限环的存在。在这种情况下，我们已经证明此类系统最多有一个交叉极限环。