The main goal of this paper is to present the behavior generated by piecewise smooth vector fields tangent to foliations. We consider two smooth foliations \(\mathcal {F}_1\) and \(\mathcal {F}_2\) that are coupled to produce a foliation composed by nested topological tori. Moreover, a piecewise smooth vector field composed of periodic orbits and tangent to these tori is considered. We perturb this piecewise vector field (and, consequently, the foliations) and the birth of either finite or infinitely many limit cycles for the 3D piecewise smooth vector field is observed.

中文翻译：

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在与嵌套环面相切的分段平滑矢量场中创建极限环

本文的主要目标是展示由与叶理相切的分段平滑矢量场产生的行为。我们考虑两个光滑的叶面\(\mathcal {F}_1\)和\(\mathcal {F}_2\)耦合以产生由嵌套拓扑环面组成的叶面。此外，还考虑了由周期轨道和这些圆环的切线组成的分段平滑矢量场。我们扰乱了这个分段矢量场（以及因此的叶理），并且观察到 3D 分段平滑矢量场的有限或无限多个极限循环的诞生。