  Instabilities in 1D spatially extended systems are studied with the aid of
both temporal and spatial Lyapunov exponents. A suitable representation of the
spectra allows a compact description of all the possible disturbances in
tangent space. The analysis is carried out for chaotic and periodic
spatiotemporal patterns. Singularities of the spectra and localization
properties of the associated Lyapunov vectors are discussed.
