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Almost sure invariance principle for nonuniformly hyperbolic systems

Melbourne, Ian and Nicol, Matthew (2005) Almost sure invariance principle for nonuniformly hyperbolic systems Communications in Mathematical Physics.

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Abstract

We prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time systems and flows are covered by this result. In particular, the result applies to the planar periodic Lorentz flow with finite horizon.

Statistical limit laws such as the central limit theorem, the law of the iterated logarithm, and their functional versions, are immediate consequences.

Item Type: Article
Additional Information: This is a pre-press version. To appear in Communications in Mathematical Physics, Springer. A link to the publisher's version of this article will appear here as soon as the paper is published.
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:41
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1444

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