Analytical Estimation of the Maximal lyapunov Exponent in Oscillator Chains
Abstract
An analytical expression for the maximal Lyapunov exponent $\lambda_1$ in generalized FermiPastaUlam 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 $\epsilon$. At very high energy density the power law scaling of $\lambda_1$ with $\epsilon$ 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 $\lambda_1 \sim \sqrt{\epsilon}$ at large $\epsilon$.
 Publication:

arXiv eprints
 Pub Date:
 February 1998
 arXiv:
 arXiv:condmat/9803001
 Bibcode:
 1998cond.mat..3001D
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks;
 Nonlinear Sciences  Chaotic Dynamics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 Latex, 10 pages, 5 Figs  Contribution to the Conference "Disorder and Chaos" held in memory of Giovanni Paladin (Sept. 1997  Rome)  submitted to J. de Physique