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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Large and moderate deviations for slowly mixing dynamical systems
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by Ian Melbourne PDF
Proc. Amer. Math. Soc. 137 (2009), 1735-1741 Request permission

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
  • 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