Israel Journal of Mathematics

, 144:191

Statistical limit theorems for suspension flows

Article

DOI: 10.1007/BF02916712

Cite this article as:
Melbourne, I. & Török, A. Isr. J. Math. (2004) 144: 191. doi:10.1007/BF02916712

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

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of Maths and StatsUniversity of SurreyGuildfordUK
  2. 2.Department of MathematicsUniversity of HoustonHoustonUSA
  3. 3.Institute of Mathematics of the Romanian AcademyBucharestRomania