Homoclinic orbits and critical points of barrier functions
  We interpret the close link between the critical points of Mather's barrier functions and minimal homoclinic orbits with respect to the Aubry sets on $\mathbb{T}^n$. We also prove a critical point theorem for barrier functions, and the existence of such homoclinic orbits on $\mathbb{T}^2$ as an application. 
Piermarco Cannarsa and Wei Cheng
math.AP