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Rate of Convergence in the Weak Invariance Principle for Deterministic Systems (1806.01204v2)
Published 4 Jun 2018 in math.DS
Abstract: We obtain the first results on convergence rates in the Prokhorov metric for the weak invariance principle (functional central limit theorem) for deterministic dynamical systems. Our results hold for uniformly expanding/hyperbolic (Axiom A) systems, as well as nonuniformly expanding/hyperbolic systems such as dispersing billiards, Henon-like attractors, Viana maps and intermittent maps. As an application, we obtain convergence rates for deterministic homogenization in multiscale systems.
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