Spurious Lyapunov Exponents Computed Using the Eckmann-Ruelle Procedure

Details Spurious Lyapunov Exponents Computed Using the Eckmann-Ruelle Procedure Spurious Lyapunov Exponents Computed Using the Eckmann-Ruelle Procedure

2000-03-02

arxiv.org/abs/nlin/0003007v1

Nonlinear Sciences

Chaotic Dynamics

Ph.D. Thesis, c. 75 pages with front matter, 13 postscript figures, 3 tables, LATEX using "rotating" and "subfigure" packages,

Scientific paper

Lyapunov exponents can be difficult to determine from experimental data. In particular, when using embedding theory to build chaotic attractors in a reconstruction space, extra "spurious" Lyapunov exponents arise that are not Lyapunov exponents of the original system. By studying the local linearization matrices that are key to the Eckmann-Ruelle 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 A and B is reconstructed in a five-dimensional space, we show that the reconstructed system has exponents A, B, 2A, A+B, 2B.

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