Topological dimension and local coordinates from time series data

Broomhead, D. S. and Jones, R. and King, Gregory P. (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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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 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry MSC 2010, the AMS's Mathematics Subject Classification > 94 Information and communication, circuits
Depositing User:	Dr Mark Muldoon
Date Deposited:	02 Mar 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/163

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