Ian Melbourne and Matthew Nicol
Abstract
We prove an almost sure invariance principle (approximation by d-dimensional Brownian motion) for vector-valued Hölder observables of large classes of nonuniformly hyperbolic dynamical systems. These systems include Axiom A diffeomorphisms and flows as well as systems modelled by Young towers with moderate tail decay rates.
In particular, the position variable of the planar periodic Lorentz gas
with finite horizon approximates a 2-dimensional Brownian motion.