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Decay of correlations in one-dimensional dynamics

Bruin, H., Luzzatto, S. and van Strien, S. (2003) Decay of correlations in one-dimensional dynamics Annales Scientifiques de l’École Normale Supérieure, 36. pp. 621-646.

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Abstract

We consider multimodal C3 interval maps f satisfying a summability condition on the derivatives Dn 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 (Dn) 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.

Item Type: Article
Additional Information: This is a pre-press version of an article published in Annales Scientifiques de l’École Normale Supérieure, 36, 621-646. Copyright © 2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Click here to visit the journal website.
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:42
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1547

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