  In this paper we examine the deviations from Gaussianity for two types of
random variable converging to a normal distribution, namely sums of random
variables generated by a deterministic discrete time map and a linearly damped
variable driven by a deterministic map. We demonstrate how Edgeworth expansions
provide a universal description of the deviations from the limiting normal
distribution. We derive explicit expressions for these asymptotic expansions
and provide numerical evidence of their accuracy.
