  We present an adaptation of Stein's method of normal approximation to the
study of both discrete- and continuous-time dynamical systems. We obtain new
correlation-decay conditions on dynamical systems for a multivariate central
limit theorem augmented by a rate of convergence. We then present a scheme for
checking these conditions in actual examples. The principal contribution of our
paper is the method, which yields a convergence rate essentially with the same
amount of work as the central limit theorem, together with a multiplicative
constant that can be computed directly from the assumptions.
