A Vector-Valued Almost Sure Invariance Principle for Hyperbolic Dynamical Systems

Details A Vector-Valued Almost Sure Invariance Principle for Hyperbolic Dynamical Systems A Vector-Valued Almost Sure Invariance Principle for Hyperbolic Dynamical Systems

2006-06-21

arxiv.org/abs/math/0606535v1

Mathematics

Dynamical Systems

Scientific paper

We prove an almost sure invariance principle (approximation by d-dimensional Brownian motion) for vector-valued Holder 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.

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