  We consider non-uniformly expanding maps on compact Riemannian manifolds of
arbitrary dimension, possibly having discontinuities and/or critical sets, and
show that under some general conditions they admit an induced Markov tower
structure for which the decay of the return time function can be controlled in
terms of the time generic points need to achieve some uniform expanding
behavior. As a consequence we obtain some rates for the decay of correlations
of those maps and conditions for the validity of the Central Limit Theorem.
