Cycle Chacterization of the Aubry Set for Weakly Coupled Hamilton-Jacobi   Systems
  We study a class of weakly coupled systems of Hamilton-acobi equations using the random frame introduced in a previous paper of Mitake-Siconolfi-Tran-Yamada. We provide a cycle condition characterizing the points of Aubry set. This generalizes a property already known in the scalar case. 
Hassan Ibrahim, Antonio Siconolfi, Sahar Zabad
math.AP