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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Large and moderate deviations for slowly mixing dynamical systems


Author: Ian Melbourne
Journal: Proc. Amer. Math. Soc. 137 (2009), 1735-1741
MSC (2000): Primary 37D25, 37A50, 60F10
Published electronically: November 26, 2008
MathSciNet review: 2470832
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Abstract: We obtain results on large deviations for a large class of nonuniformly hyperbolic dynamical systems with polynomial decay of correlations $ 1/n^\beta$, $ \beta>0$. This includes systems modelled by Young towers with polynomial tails, extending recent work of M. Nicol and the author which assumed $ \beta>1$. As a byproduct of the proof, we obtain slightly stronger results even when $ \beta>1$. The results are sharp in the sense that there exist examples (such as Pomeau-Manneville intermittency maps) for which the obtained rates are best possible. In addition, we obtain results on moderate deviations.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09751-7
PII: S 0002-9939(08)09751-7
Received by editor(s): June 9, 2008
Published electronically: November 26, 2008
Additional Notes: This research was supported in part by EPSRC Grant EP/D055520/1.
Communicated by: Bryna Kra
Article copyright: © Copyright 2008 American Mathematical Society