Analytical Estimation of the Maximal lyapunov Exponent in Oscillator Chains [article]

Thierry Dauxois, Stefano Ruffo, Alessandro Torcini
1998 arXiv   pre-print
An analytical expression for the maximal Lyapunov exponent λ_1 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 λ_1 with ϵ can be also obtained by simple dimensional arguments, assuming that the
more » ... stem is ruled by a single time scale. Finally, we argue that for repulsive and hard core potentials in one dimension λ_1 ∼√(ϵ) at large ϵ.
arXiv:cond-mat/9803001v1 fatcat:75jhs3ulhngmhosyed37vyq22q