On almost-sure versions of classical limit theorems for dynamical systems

Details On almost-sure versions of classical limit theorems for dynamical systems On almost-sure versions of classical limit theorems for dynamical systems

2006-01-16

arxiv.org/abs/math/0601388v2

Mathematics

Dynamical Systems

41 pages; submitted v2: replaced the argument for Gibbs-Markov maps with a general spectral argument

Scientific paper

The purpose of this article is to construct a toolbox, in Dynamical Systems, to support the idea that ``whenever we can prove a limit theorem in the classical sense for a dynamical system, we can prove a suitable almost-sure version based on an empirical measure with log-average''. We follow three different approaches: martingale methods, spectral methods and induction arguments. Our results apply among others to Axiom A maps or flows, to systems inducing a Gibbs-Markov map and to the stadium billiard.

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