J. Phys. IV France 08 (1998) Pr6-147-Pr6-156
Analytical estimation of the maximal Lyapunov exponent in oscillator chainsT. Dauxois1, 2, 3, S. Ruffo1 and A. Torcini1
1 Dipartimento di Energetica S. Stecco, via S. Marta 3, 50139 Firenze, Italy
2 Scripps Institution of Oceanography, University of California at San Diego, La Jolla CA 92093-0230, U.S.A.
3 Laboratoire de Physique, ENS Lyon, URA 1325 du CNRS, 69364 Lyon cedex 07, France
An analytical expression for the maximal Lyapunov exponent λ1 in generalized Fermi-Pasta-Ulam oscillator chains is obtained. The derivation is based on the calculation of modulational instability growth rates for some unstable periodic orbits. The result is compared with numerical simulations and the agreement is good over a wide range of energy densities ε. At very high energy density the power law scaling of λ1 with ε can be also obtained by simple dimensional arguments, assuming that the system is ruled by a single time scale. Finally, we argue that for repulsive and hard core potentials in one dimension λ1 ≈ ε0.5 at large ε.
© EDP Sciences 1998