Large and moderate deviations for slowly mixing dynamical systems

Melbourne, Ian

doi:10.1090/S0002-9939-08-09751-7

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.

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