Chaos in Piecewise Smooth Vector Fields on Two Dimensional Torus and   Sphere
  In this paper we study the global dynamics of piecewise smooth vector fields defined in the two dimensional torus and sphere. We provide conditions under these families exhibits periodic and dense trajectories and we describe some global bifurcations. We also study its minimal sets and characterize the chaotic behavior of the piecewise smooth vector fields defined in torus and sphere. 
Ricardo Miranda Martins and Durval Jos\'e Tonon
math.DS