  We prove several limit theorems for a simple class of partially hyperbolic
fast-slow systems. We start with some well know results on averaging, then we
give a substantial refinement of known large (and moderate) deviation results
and conclude with a completely new result (a local limit theorem) on the
distribution of the process determined by the fluctuations around the average.
The method of proof is based on a mixture of standard pairs and Transfer
Operators that we expect to be applicable in a much wider generality.
