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Journal of the London Mathematical Society Advance Access originally published online on September 29, 2007
Journal of the London Mathematical Society 2007 76(2):345-364; doi:10.1112/jlms/jdm060
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© 2007 London Mathematical Society

Central limit theorems and invariance principles for Lorenz attractors

Mark Holland and Ian Melbourne

Department of Mathematics and Statistics
University of Surrey
Guildford
Surrey
GU2 7XH
United Kingdom

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.

2000 Mathematics Subject Classification 37A50 (primary), 37D25, 37C40 (secondary).

Current address: School of Engineering, Computer Science and Mathematics Harrison Building North Park Road Exeter EX4 4OF United Kingdom m.p.holland{at}exeter.ac.uk

Received March 7, 2006; revised November 22, 2006; published online October 29, 2007.


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