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Mathematics

The Lorenz attractor exists

Nature volume 406, pages 948–949 (2000)Cite this article

Tucker's work is hugely significant, not just because it provides the Lorenz attractor with a solid foundation, but because his techniques will be widely applicable. At last, the embarrassing gap between what we think we know about a nonlinear dynamical system from numerical simulations, and what we actually know in full logical rigour, is starting to close. At the moment the methods are limited to dynamics in three dimensions, but after Tucker's breakthrough that may well change. Dimensions greater than three are of considerable interest because the dimension of a dynamical system is not the dimension of ordinary space, but the number of variables in the equations. For example, the motion of a three-body system consisting of the Earth, Mars and a space probe requires six variables for each body — three of position and three of velocity — and so is an 18-dimensional dynamical system.

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Figure 1: The Lorenz attractor was first derived from a simple model of convection in the Earth's atmosphere.

PAUL BOURKE, SWINBURNE UNIV. TECHNOL.

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  1. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

    Ian Stewart

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Correspondence to Ian Stewart.

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Stewart, I. The Lorenz attractor exists. Nature 406, 948–949 (2000). https://doi.org/10.1038/35023206

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