Monday, May 8, 2017 - 11:00
1 hour (actually 50 minutes)
We will consider the Frenkel-Kontorova models and their higher dimensional generalizations and talk about the corresponding discrete weak KAM theory. The existence of the discrete weak KAM solutions is related to the additive eigenvalue problem in ergodic optimization. In particular, I will show that the discrete weak KAM solutions converge to the weak KAM solutions of the autonomous Tonelli Hamilton-Jacobi equations as the time step goes to zero.