Decay of correlations in one-dimensional dynamics

Bruin, Henk; Luzzatto, Stefano; van Strien, Sebastian

Decay of correlations in one-dimensional dynamics

Authors

Bruin, Henk

Luzzatto, Stefano

van Strien, Sebastian

Description

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 tends to 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.
To appear in Annales de l'Ecole Normale Superieure, 2002