Rapid decay of correlations for nonuniformly hyperbolic flows
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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.References
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Additional Information
- Ian Melbourne
- Affiliation: Department of Mathematics and Statistics, University of Surrey, Guildford GU2 7XH, United Kingdom
- MR Author ID: 123300
- Email: ism@math.uh.edu
- 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.
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 2421-2441
- MSC (2000): Primary 37A25, 37D25, 37D50
- DOI: https://doi.org/10.1090/S0002-9947-06-04267-X
- MathSciNet review: 2276628