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Statistical Limit theorems for suspension flows

Melbourne, Ian and Török, Andrei (2004) Statistical Limit theorems for suspension flows Israel Journal of Math, 144 (2004). pp. 191-209.

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Abstract

In dynamical systems theory, a standard method for passing from discrete time to continuous time is to construct the suspension flow under a roof function. In this paper, we give conditions under which statistical laws, such as the central limit theorem and almost sure invariance principle, for the underlying discrete time system are inherited by the suspension flow. As a consequence, we give a simpler proof of the results of Ratner (1973) and recover the results of Denker and Philipp (1984) for Axiom A flows. Moreover, we obtain several new results for nonuniformly and partially hyperbolic flows, including frame flows on negatively curved manifolds satisfying a pinching condition.

Item Type: Article
Additional Information: Israel Journal of Math. 144 (2004) 191-209
Uncontrolled Keywords: dynamical systems, descrete time, continuous time, hyperbolic flows
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:40
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1426

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