Spurious Lyapunov exponents computed from data

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