On piecewise smooth vector fields tangent to nested tori

In this paper we present a number of results involving 3D nonsmooth dynamical systems tangent to a foliation. We study one-parameter families of systems ZεZε passing through a specific model Z0Z0 whose phase portrait is foliated by invariant nested tori. For each positive integer k   we, explicitly, construct a family Zεk possessing exactly k nested tori.