ANALYTICAL ESTIMATION OF THE MAXIMAL LYAPUNOV EXPONENT IN OSCILLATOR CHAINS

An analytical expression for the maximal Lyapunov exponent lambda(1) i n generalized Fermi-Pasta-Ulam oscillator chains is obtained. The deri vation is based on the calculation of modulational instability growth rates for some unstable periodic orbits. The result is compared with n umerical simulations and the agreement is good over a wide range of en ergy densities epsilon. At very high energy density the power law scal ing of lambda(1) with epsilon can be also obtained by simple dimension al arguments, assuming that the system is ruled by a single time scale . Finally, we argue that for repulsive and hard fore potentials in one dimension lambda(1) similar to root epsilon at large epsilon.