Melbourne, Ian and Nicol, Matthew (2008) Large deviations for nonuniformly hyperbolic systems. Transactions of the American Mathematical Society, Vol.360 (No.12). pp. 6661-6676. doi:10.1090/S0002-9947-08-04520-0 ISSN 0002-9947.

Research output not available from this repository.

Request-a-Copy directly from author or use local Library Get it For Me service.

Request Changes to record.

Abstract

We obtain large deviation estimates for a large class of nonuniformly hyperbolic systems: namely those modelled by Young towers with summable decay of correlations. In the case of exponential decay of correlations, we obtain exponential large deviation estimates given by a rate function. In the case of polynomial decay of correlations, we obtain polynomial large deviation estimates, and exhibit examples where these estimates are essentially optimal.

In contrast with many treatments of large deviations, our methods do not rely on thermodynamic formalism. Hence, for Hölder observables we are able to obtain exponential estimates in situations where the space of equilibrium measures is not known to be a singleton, as well as polynomial estimates in situations where there is not a unique equilibrium measure.

Item Type:	Journal Article
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Transactions of the American Mathematical Society
Publisher:	American Mathematical Society
ISSN:	0002-9947
Official Date:	2008
Dates:	Date Event 2008 Published
Volume:	Vol.360
Number:	No.12
Page Range:	pp. 6661-6676
DOI:	10.1090/S0002-9947-08-04520-0
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

Request changes or add full text files to a record

Repository staff actions (login required)

View Item