Iterates of expanding maps

The iterates of expanding maps of the unit interval into itself have many o f the properties of a more conventional stochastic process, when the expand ing map satisfies some regularity conditions and when the starting point is suitably chosen at random. In this paper, we show that the sequence of ite rates can be closely tied to an m-dependent process. This enables us to pro ve good bounds on the accuracy of Gaussian approximations. Our main tools a re coupling and Stein's method.