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2006.18: Topological dimension and local coordinates from time series data

2006.18: D. S. Broomhead, R. Jones and Gregory P. King (1987) Topological dimension and local coordinates from time series data. Journal of Physics A, 20 (9). L563-L569. ISSN 0305-4470

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DOI: 10.1088/0305-4470/20/9/003

Abstract

A method for the estimation of the topological dimension of a manifold from time series data is presented. It is based on the approximation of the manifold near a point chi by its tangent space at chi. The dimension of the tangent space is estimated by constructing a maximal set of linearly independent vectors from the data near chi using the method of singular value decomposition. The method is used to analyse experimental data obtained from a nonlinear electronic oscillator in a chaotic state.

Item Type:Article
Uncontrolled Keywords:time series, delay embedding, singular value decomposition, dimension
Subjects:MSC 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 53 Differential geometry
MSC 2000 > 94 Information and communication, circuits
MIMS number:2006.18
Deposited By:Dr Mark Muldoon
Deposited On:02 March 2006

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