Israel Journal of Mathematics

, Volume 144, Issue 2, pp 191-209

First online:

Statistical limit theorems for suspension flows

  • Ian MelbourneAffiliated withDepartment of Maths and Stats, University of Surrey Email author 
  • , Andrei TörökAffiliated withDepartment of Mathematics, University of HoustonInstitute of Mathematics of the Romanian Academy

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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. Morcover, we obtain several new results for nonuniformly and partially hyperbolic flows, including frame flows on negatively curved manifolds satisfying a pinching condition.