Decay of correlations in one-dimensional dynamics

Abstract

We consider multimodal C 3 interval maps f satisfying a summability condition on the derivatives D n along the critical orbits which implies the existence of an absolutely continuous f-invariant probability measure μ. If f is non-renormalizable, μ is mixing and we show that the speed of mixing (decay of correlations) is strongly related to the rate of growth of the sequence ( D n ) as n→∞. We also give sufficient conditions for μ to satisfy the Central Limit Theorem. This applies for example to the quadratic Fibonacci map which is shown to have subexponential decay of correlations.