The problem of spurious Lyapunov exponents in time series analysis and its solution by covariant Lyapunov vectors

We briefly recall the methods for the determination of Lyapunov exponents from time series data and their limitations. One particular problem is given by the fact that reconstructed phase spaces have usually extra dimensions compared to the true phase space of a dynamical system, leading to extra, so called spurious Lyapunov exponents. Several methods to identify the true ones have been proposed which do not give satisfactory results. We show that the geometric information contained in covariant Lyapunov vectors can be used to identify the true exponents. We illustrate its use and its limitations by applying it to experimental NMR laser data.