Central Limit Theorems and Invariance Principles for Lorenz Attractors

J London Math Soc 76 (2007) 345-364

Mark Holland and Ian Melbourne


Abstract


We prove statistical limit laws for Hölder observations of the Lorenz attractor, and more generally for geometric Lorenz attractors. In particular, we prove the almost sure invariance principle (approximation by Brownian motion). Standard consequences of this result include the central limit theorem, the law of the iterated logarithm, and the functional versions of these results.
Postscript file or pdf file