  The computation of the entire Lyapunov spectrum for extended dynamical
systems is a very time consuming task. If the system is in a chaotic
spatio-temporal regime it is possible to approximately reconstruct the Lyapunov
spectrum from the spectrum of a sub-system in a very cost effective way. In
this work we present a new rescaling method, which gives a significantly better
fit to the original Lyapunov spectrum. It is inspired by the stability analysis
of the homogeneous evolution in a one-dimensional coupled map lattice but
appears to be equally valid in a much wider range of cases. We evaluate the
performance of our rescaling method by comparing it to the conventional
rescaling (dividing by the relative sub-system volume) for one and
two-dimensional lattices in spatio-temporal chaotic regimes. In doing so we
notice that the Lyapunov spectra for consecutive sub-system sizes are
interleaved and we discuss the possible ways in which this may arise. Finally,
we use the new rescaling to approximate quantities derived from the Lyapunov
spectrum (largest Lyapunov exponent, Lyapunov dimension and Kolmogorov-Sinai
entropy) finding better convergence as the sub-system size is increased than
with conventional rescaling.
