Decay of correlations in a chaotic measure-preserving transformation

Abstract For a chaotic, area-preserving map on the torus, we study the decay of correlations in detail. Taking as observables the square-integrable functions, we find examples of decay rates which are algebraic, exponential, and faster than exponential. For correlations that decay exponentially the rate is sensitive to the choice of function. The implications for numerical experiments of this nonuniformity in the decay are discussed.