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.
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.
|Additional Information:||First published in Transactions of the American Mathematical Society, 359, 2421-2441. Published by the American Mathematical Society. Copyright American Mathematical Society 2007.|
|Divisions:||Faculty of Engineering and Physical Sciences > Mathematics|
|Deposited By:||Mr Adam Field|
|Deposited On:||27 May 2010 15:40|
|Last Modified:||28 Sep 2012 10:50|
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