Analytical Estimation of the Maximal lyapunov Exponent in Oscillator Chains

@article{Dauxois1998AnalyticalEO,
  title={Analytical Estimation of the Maximal lyapunov Exponent in Oscillator Chains},
  author={Thierry Dauxois and Stefano Ruffo and Alessandro Torcini},
  journal={Journal De Physique Iv},
  year={1998},
  volume={08},
  pages={147-156}
}
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 e At very high energy density the power law scaling of λ 1 with e can be also obtained by simple dimensional arguments, assuming that the… 
5 Citations

Figures from this paper

Measures of chaos and equipartition in integrable and nonintegrable lattices.
TLDR
The discretized Riemann invariants of the alpha lattice reveal soliton and near-soliton properties for acoustic excitations in one-dimensional FPU-alpha and Toda lattices.
The anti-FPU problem.
TLDR
It is shown that breathers formed when cooling the lattice at the edges, starting from a random initial state, bear strong qualitative similarities with chaotic breathers.
Modulational instability in isolated and driven Fermi–Pasta–Ulam lattices
Abstract.We present a detailed analysis of the modulational instability of the zone-boundary mode for one and higher-dimensional Fermi–Pasta–Ulam (FPU) lattices. The growth of the instability is
Backbone curves, Neimark-Sacker boundaries and appearance of quasi-periodicity in nonlinear oscillators: application to 1:2 internal resonance and frequency combs in MEMS
Quasi-periodic solutions can arise in assemblies of nonlinear oscillators as a consequence of Neimark-Sacker bifurcations. In this work, the appearance of Neimark-Sacker bifurcations is investigated
Significant improvement of soft magnetic properties for Fe(Co)BPSiC amorphous alloys by magnetic field annealing
Abstract Longitudinal field annealing (FA) is used to improve the soft magnetic properties (SMPs) of Fe83-xCoxB11P3Si2C1 (x = 0–20) amorphous alloys with high Bs of 1.65–1.76 T. These amorphous

References

SHOWING 1-10 OF 49 REFERENCES
Regular and Chaotic Dynamics
This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to
Products of random matrices in statistical physics
I Background.- 1. Why Study Random Matrices?.- 1.1 Statistics of the Eigenvalues of Random Matrices.- 1.1.1 Nuclear Physics.- 1.1.2 Stability of Large Ecosystems.- 1.1.3 Disordered Harmonic Solids.-
Dynamics of the liquid state
1. The basic dynamical quantitites 2. The experimental side 3. General theoretical framework 4. Generalized kinetic theory 5. Single-particle properties 6. Collective properties Appendices Index
Physica D 104
  • 148
  • 1997
Ruffo Physica D
  • Ruffo Physica D
  • 1997
Phys
  • Rev. Lett. 74, 375
  • 1995
Phys. Rev. Lett
  • Phys. Rev. Lett
  • 1995
Nonlinearity
  • Nonlinearity
  • 1997
Nonlinearity 10
  • 617
  • 1997
Phys
  • Rev. E 56, R6229
  • 1997
...
1
2
3
4
5
...