Let $\Sigma_{ A}(\mathbb{ N})$ be a topologically mixing countable Markov shift with the BIP property over the alphabet $\mathbb{ N}$ and $f: \Sigma_{ A}(\mathbb{ N}) \rightarrow \mathbb{ R}$ a potential satisfying the Walters condition with finite Gurevich pressure. Under suitable hypotheses, we prove the existence of a Large Deviation Principle for the family $(\mu_{ \beta})_{ \beta > 0}$ where each $\mu_{ \beta}$ is the Gibbs measure associated to the potential $\beta f$. Our main theorem generalizes from finite to countable alphabets and also to a larger class of potentials a previous result of A. Baraviera, A. O. Lopes and P. Thieullen.
Categories: math.DS