Lyapunov spectrum analysis of reconstructed attractors from observed time series

We analyze effect of extra reconstructed dimensions on Lyapunov spectrum, which includes spurious Lyapunov exponents, of unknown dynamical systems. An emphasis of this paper is on that the result obtained by the new analysis may provide an evidence against the previously reported result. It is shown that the spurious exponents can be discriminated from the true exponents of the unknown dynamical system, and thus the dimension of the unknown dynamical system can be estimated by using the new analysis.