  We present here a general iterative formula which gives a (formal) series
expansion for the time autocorrelation of smooth dynamical variables, for all
Hamiltonian systems endowed with an invariant measure. We add some criteria,
theoretical in nature, which enable one to decide whether the decay of the
correlations is exponentially fast or not. One of these criteria is implemented
numerically for the case of the Fermi-Pasta-Ulam system, and we find
indications which might suggest a sub-exponential decay of the time
autocorrelation of a relevant dynamical variable.
