Selection of calibrated subaction when temperature goes to zero in the discounted problem

Renato Iturriaga, Artur O. Lopes, Jairo K. Mengue

Consider $T(x)=dx$ (mod 1) acting on $S^1$, a Lipschitz potential $A:S^1\to \mathbb{R}$, $0<\lambda <1$ and the unique function $b_{\lambda }:S^1\to \mathbb{R}$ satisfying $ b_λ(x) = \max_{…