A proof that all the sliding trajectories of generic inelastic piecewise linear dynamical systems over the torus are closed

Mayara D. A. Caldas, Ricardo M. Martins

In this article, we consider piecewise smooth differential equations $Z_{X_{-}{X}_{+}}$, where $X_{-}$ and $X_{+}$ are linear vector fields in dimension 3, having the torus as discontinuity…