Weak KAM methods and ergodic optimal problems for countable Markov shifts

Rodrigo Bissacot, Eduardo Garibaldi

Let $\sigma :\mathbf{\Sigma }\to \mathbf{\Sigma }$ be the left shift acting on $\mathbf{\Sigma }$, a one-sided Markov subshift on a countable alphabet. Our intention is to guarantee the existence o…