Statistical properties for flows with unbounded roof function, including the Lorenz attractor

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.

Minor corrections. Published online in J. Stat. Phys

References in corpus (1)

• Polynomial decay of correlations for flows, including Lorentz gas examples

Cited by in corpus (8)

• Polynomial decay of correlations for flows, including Lorentz gas examples
• Rate of Convergence in the Weak Invariance Principle for Deterministic Systems
• Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas
• Robust parameter estimation using the ensemble Kalman filter
• Finitely many physical measures for sectional-hyperbolic attracting sets and statistical stability
• Rough McKean-Vlasov dynamics for robust ensemble Kalman filtering
• Fluctuations of time averages around closed geodesics in non-positive curvature
• Exponential mixing for singular skew-products