Topological dimension and local coordinates from time series data

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.