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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Rapid decay of correlations for nonuniformly hyperbolic flows


Author: Ian Melbourne
Journal: Trans. Amer. Math. Soc. 359 (2007), 2421-2441
MSC (2000): Primary 37A25, 37D25, 37D50
Published electronically: December 5, 2006
MathSciNet review: 2276628
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Abstract | References | Similar Articles | Additional Information

Abstract: 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.


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Additional Information

Ian Melbourne
Affiliation: Department of Mathematics and Statistics, University of Surrey, Guildford GU2 7XH, United Kingdom
Email: ism@math.uh.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-06-04267-X
PII: S 0002-9947(06)04267-X
Received by editor(s): January 31, 2005
Received by editor(s) in revised form: July 14, 2005
Published electronically: December 5, 2006
Additional Notes: This research was supported in part by EPSRC Grant GR/S11862/01. Technological support by the University of Houston is gratefully acknowledged.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.