Journal
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
Volume 6, Issue 2, Pages 457-474Publisher
SIAM PUBLICATIONS
DOI: 10.1137/040619211
Keywords
Lyapunov exponents; embedding; time-series analysis; attractor reconstruction
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Lyapunov exponents can be di. cult to determine from experimental data. In particular, when using embedding theory to build chaotic attractors in a reconstruction space, extra spurious Lyapunov exponents can arise that are not Lyapunov exponents of the original system. By studying the local linearization matrices that are key to a popular method for computing Lyapunov exponents, we determine explicit formulas for the spurious exponents in certain cases. Notably, when a two-dimensional system with Lyapunov exponents lambda and mu is reconstructed in a five-dimensional space by a generic embedding, the reconstructed system has exponents lambda, mu, 2 lambda,+ mu, and 2 mu. In particular, when mu < 0
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