Calculation of Lyapunov exponents avoiding spurious elements (Q808497)

An approach for estimating Lyapunov exponents from time series is discussed. Assuming knowledge of the integral dimension of the attractor imagined behind the time series, the approach proceeds by modifying the usual approximations of the tangent map from the time series (for a given embedding dimension) as follows. Only a certain number - corresponding to the dimension of the attractor - of leading singular values are kept. All further singular values are set zero by force at each step. This both avoids `spurious exponents' and speeds up calculations. The performance of the method is illustrated by applying it to simulated data.