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.
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.
|Divisions :||Faculty of Engineering and Physical Sciences > Mathematics|
|Date :||26 August 2003|
|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.|
|Depositing User :||Mr Adam Field|
|Date Deposited :||27 May 2010 14:42|
|Last Modified :||23 Sep 2013 18:33|
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