Statistical Properties for Flows with Unbounded Roof Function,Including the Lorenz Attractor |
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Authors: | Péter Bálint Ian Melbourne |
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Institution: | 1.MTA-BME Stochastics Research Group,Budapest University of Technology and Economics,Budapest,Hungary;2.Department of Stochastics, Institute of Mathematics,Budapest University of Technology and Economics,Budapest,Hungary;3.Mathematics Institute,University of Warwick,Coventry,UK |
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Abstract: | For geometric Lorenz attractors (including the classical Lorenz attractor) we obtain a greatly simplified proof of the central limit theorem which applies also to the more general class of codimension two singular hyperbolic attractors. We also obtain the functional central limit theorem and moment estimates, as well as iterated versions of these results. A consequence is deterministic homogenisation (convergence to a stochastic differential equation) for fast-slow dynamical systems whenever the fast dynamics is singularly hyperbolic of codimension two. |
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