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Rapid Decay of Correlations for Nonuniformly Hyperbolic Flows

Melbourne, Ian (2007) Rapid Decay of Correlations for Nonuniformly Hyperbolic Flows Transactions of the American Mathematical Society, 359. pp. 2421-2441.


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We show that superpolynomial decay of correlations (rapid mixing) is prevalent for a class of nonuniformly hyperbolic flows. These flows are the continuous time analogue of the class of nonuniformly hyperbolic maps for which Young proved exponential decay of correlations. The proof combines techniques of Dolgopyat and operator renewal theory. It follows from our results that planar periodic Lorentz flows with finite horizons and flows near homoclinic tangencies are typically rapid mixing.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Date : 1 January 2007
Additional Information : Melbourne, I. (2007) Rapid Decay of Correlations for Nonuniformly Hyperbolic Flows. First published in <i>Transactions of the American Mathematical Society,</i> in Vol 359, No. 5, pp. 2421-2441. Published by the American Mathematical Society. Article electronically published on December 5, 2006 &amp;copy AMS Click <a href= >here</a> to visit the journal's website
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:40
Last Modified : 06 Jul 2019 05:06

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