Phase-space reconstruction in Hamiltonian systems through multiple time series

Abstract

A method which combines the various time series originating from a single source in order to reconstruct the phase-space dynamics is applied to a chaotic Hamiltonian system. It is shown that for a large energy range the variation of the maximum Lyapunov exponents can be reproduced more accurately than the results obtained from a single time series, for both clean and noisy signals. Especially in cases where the maximum exponent is close to zero, using multiple series can give better results, providing a more reliable way of detecting chaos.