  We consider two compact metric spaces $J$ and $X$ and a uniform contractible
iterated function system $\{\phi_j: X \to X \, | \, j \in J \}$. For a
Lipschitz continuous function $A$ on $J \times X$ and for each $\beta>0$ we
consider the Gibbs probability $\rho_{_{\beta A}}$. Our goal is to study a
large deviation principle for such family of probabilities as $\beta \to
+\infty$ and its connections with idempotent probabilities. In the non-place
dependent case ($A(j,x)=A_j,\,\forall x\in X$) we will prove that
$(\rho_{_{\beta A}})$ satisfy a LDP and $-I$ (where $I$ is the deviation
function) is the density of the unique invariant idempotent probability for a
mpIFS associated to $A$. In the place dependent case, we prove that, if
$(\rho_{_{\beta A}})$ satisfy a LDP, then $-I$ is the density of an invariant
idempotent probability. Such idempotent probabilities were recently
characterized through the Ma\~{n}\'{e} potential and Aubry set, therefore we
will obtain an identical characterization for $-I$.
