Creation of Limit Cycles in Piecewise Smooth Vector Fields Tangent to Nested Tori

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 F1 and F2 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.

Automated summary

This paper aims to explore the behavior generated by piecewise smooth vector fields tangent to foliations, particularly in the case of two smooth foliations coupled to form nested topological tori. Perturbing a piecewise smooth vector field and foliations may lead to the formation of either finite or infinitely many limit cycles for the 3D system.