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 beta model (1955). The authors show that the shape of the spectrum for energy density well above the equipartition threshold epsilon c allows the Kolmogorov Sinai entropy to be expressed simply in terms of the maximum exponent lambda max. The presence of a power-law behaviour epsilon beta 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.