## Large and moderate deviations for slowly mixing dynamical systems

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- by Ian Melbourne
- Proc. Amer. Math. Soc.
**137**(2009), 1735-1741 - DOI: https://doi.org/10.1090/S0002-9939-08-09751-7
- Published electronically: November 26, 2008
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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.## References

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## Bibliographic Information

**Ian Melbourne**- Affiliation: Department of Mathematics, University of Surrey, Guildford GU2 7XH, United Kingdom
- MR Author ID: 123300
- Email: ism@math.uh.edu
- 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
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**137**(2009), 1735-1741 - MSC (2000): Primary 37D25, 37A50, 60F10
- DOI: https://doi.org/10.1090/S0002-9939-08-09751-7
- MathSciNet review: 2470832