On Determining the Dimension of Chaotic Flows

Harold Froehling
James P. Crutchfield
Doyne Farmer
N. H. Packard
Rob Shaw

Physcis Department
Univeristy of California
Santa Cruz, CA 95064, USA

Abstract

We describe a method for determining the approximate fractal dimension of an attractor. Our technique fits linear subspaces of appropriate dimension to sets of points on the attractor. The deviation between points on the attractor and this local linear subspace is analyzed through standard multilinear regressoin techniques. We show how the local dimension of attractors underlying physical phenomena can be measured even when only a single time-varying quantity is available for analysis. These methods are applied to several dissipative dynamical systems.

Citation

H. Froehling, J. P. Crutchfield, J. D. Farmer, N. H. Packard, and R. S. Shaw. "On Determining the Dimension of Chaotic Flows." Physica 3D 1981: 605-617.

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