Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 maps
Dynamical Systems
2016-11-24 v5 Mathematical Physics
Classical Analysis and ODEs
math.MP
Abstract
We prove that every geometric Lorenz attractor has superpolynomial decay of correlations with respect to the unique SRB measure. Moreover, we prove the Central Limit Theorem and Almost Sure Invariance Principle for the time-1 map of the flow of geometric Lorenz attractors. In particular, our results apply to the classical Lorenz attractor.
Keywords
Cite
@article{arxiv.1311.5017,
title = {Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 maps},
author = {V. Araujo and I. Melbourne and P. Varandas},
journal= {arXiv preprint arXiv:1311.5017},
year = {2016}
}
Comments
30 pages, 3 figures. Final accepted version to appear in Communications in Math Phys