Distribution of characteristic exponents in the thermodynamic limit

The existence of the thermodynamic limit for the spectrum of the Lyapunov characteristic exponents is numerically investigated for the Fermi-Pasta-Ulam p model. We show that the shape of the spectrum for energy density well above the equipartition threshold E, allows the Kolmogorov-Sinai entropy to be expressed simply in terms of the maximum exponent I,,,. The presence of a power-law behaviour E@ is investigated. The analogies with similar results obtained from the dynamics of symplectic random matrices seem to indicate the possibility of interpreting chaotic dynamics in terms of some 'universal' properties.