Quasidiagonal approach to the estimation of Lyapunov spectra for spatiotemporal systems from multivariate time series

We describe methods of estimating the entire Lyapunov spectrum of a spatial ly extended system from multivariate time-series observations. Provided tha t the coupling in the system is short range, the Jacobian has a banded stru cture and can be estimated using spatially localized reconstructions in low embedding dimensions. This circumvents the "curse of dimensionality" that prevents the accurate reconstruction of high-dimensional dynamics from obse rved time series. The technique is illustrated using coupled map lattices a s prototype models for spatiotemporal chaos and is found to work even when the coupling is not strictly local but only exponentially decaying.