  The Central Limit Theorem states that, in the limit of a large number of
terms, an appropriately scaled sum of independent random variables yields
another random variable whose probability distribution tends to a stable
distribution. The condition of independence, however, only holds in real
systems as an approximation. To extend the theorem to more general situations,
previous studies have derived a version of the Central Limit Theorem that also
holds for variables that are not independent. Here, we present numerical
results that characterize how convergence is attained when the variables being
summed are deterministically related to one another by the recurrent
application of an ergodic mapping. In all the explored cases, the convergence
to the limit distribution is slower than for random sampling. Yet, the speed at
which convergence is attained varies substantially from system to system, and
these variations imply differences in the way information about the
deterministic nature of the dynamics is progressively lost as the number of
summands increases. Some of the identified factors in shaping the convergence
process are the strength of mixing induced by the mapping and the shape of the
marginal distribution of each variable, most particularly, the presence of
divergences or fat tails.
