Lyapunov exponents from unstable periodic orbits in the FPU-beta model

Details Lyapunov exponents from unstable periodic orbits in the FPU-beta model Lyapunov exponents from unstable periodic orbits in the FPU-beta model

2004-08-30

arxiv.org/abs/nlin/0408056v1

Nonlinear Sciences

Chaotic Dynamics

6 PAGES, 3 FIGURES

Scientific paper

In the framework of a recently developed theory for Hamiltonian chaos, which makes use of the formulation of Newtonian dynamics in terms of Riemannian differential geometry, we obtained analytic values of the largest Lyapunov exponent for the Fermi-Pasta-Ulam-beta model (FPU-beta) by computing the time averages of the metric tensor curvature and of its fluctuations along analytically known unstable periodic orbits (UPOs). The agreement between our results and the Lyapunov exponents obtained by means of standard numerical simulations supports the fact that UPOs are reliable probes of a general dynamical property as chaotic instability.

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