Lyapunov exponents and rates of mixing for one-dimensional maps

Abstract

We show that one-dimensionalmaps f with strictly positive Lyapunov exponents almost everywhere admit an absolutely continuous invariantmeasure. If f is topologically transitive, some power of f is mixing and, in particular, the correlation of H¨older continuous observables decays to zero. The main objective of this paper is to show that the rate of decay of correlations is determined, in some situations, by the average rate at which typical points start to exhibit exponential growth of the derivative.