Spurious Lyapunov Exponents Computed Using the Eckmann - Ruelle Procedure
نویسندگان
چکیده
Lyapunov exponents, important invariants of a complicated dynamical process, 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 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 α and β is reconstructed in a five-dimensional space, we show that the reconstructed system has exponents α, β, 2α, 2β, and α + β. SPURIOUS LYAPUNOV EXPONENTS
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