  In the framework of the Fermi-Pasta-Ulam (FPU) model, we show a simple method
to give an accurate analytical estimation of the maximal Lyapunov exponent at
high energy density. The method is based on the computation of the mean value
of the modulational instability growth rates associated to unstable modes.
Moreover, we show that the strong stochasticity threshold found in the
$\beta$-FPU system is closely related to a transition in tangent space: the
Lyapunov eigenvector being more localized in space at high energy.
