Large Deviations for Countable to One Markov Systems

In this paper, we study large deviation properties for countable to one Markov systems associated to weak Gibbs measures for non-Holder potentials. Furthermore, we establish multifractal large deviation laws for countable to one piecewise conformal Markov systems, which are derived systems constructed over hyperbolic regions for certain nonhyperbolic systems exhibiting intermittency. We apply our results to higher-dimensional number theoretical transformations.