Decay of correlations in one-dimensional dynamics

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 mu. If f is non-renormalizable, mu 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 --> infinity. We also give sufficient conditions for mu to satisfy the Central Limit Theorem. This applies for example to the quadratic Fibonacci map which is shown to have subexponential decay of correlations. (C) 2003 Editions scientifiques et medicales Elsevier SAS.