Decay of correlations in one-dimensional dynamics
Dynamical Systems
2007-05-23 v1 Mathematical Physics
math.MP
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 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.
Cite
@article{arxiv.math/0208114,
title = {Decay of correlations in one-dimensional dynamics},
author = {Henk Bruin and Stefano Luzzatto and Sebastian van Strien},
journal= {arXiv preprint arXiv:math/0208114},
year = {2007}
}
Comments
To appear in Annales de l'Ecole Normale Superieure, 2002