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Singular-value decomposition in attractor reconstruction: Pitfalls and precautions. (English) Zbl 0744.58046

Summary: Applicability of singular-value decomposition for reconstructing the strange attractor from one-dimensional chaotic time series, proposed by Broomhead and King, is extensively tested and discussed. Previously published doubts about its reliability are confirmed: singular-value decomposition, by nature a linear method, can bring distorted and misleading results when nonlinear structures are studied.

MSC:

37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37A99 Ergodic theory
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