Israel Journal of Math. 144 (2004) 191-209
Ian Melbourne and Andrew Török
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, and we obtain new results on nonuniformly and partially hyperbolic flows.