Geometry from a Time Series

N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw
Physics Board of Studies
University of California
Santa Cruz, California 95064 USA

Abstract

It is shown how the existence of low-dimensional chaotic dynamical systems describing turbulent fluid flow might be determined experimentally. Techniques are outlined for reconstructing phase-space pictures from the observables of a single coordinate of any dissipative dynamical system, and for determining the dimensionality of the system's attractor. These techniques are applied to a well-known simple three-dimensional chaotic dynamical system.

Citation

N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw, Geometry from a Time Series, Phys. Rev. Let. 45 (1980) 712-716.

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