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Gaussian Model for Chaotic Instability of Hamiltonian Flows

1995; American Physical Society; Volume: 74; Issue: 3 Linguagem: Inglês

10.1103/physrevlett.74.375

1092-0145

Lapo Casetti, Roberto Livi, Marco Pettini,

Advanced Thermodynamics and Statistical Mechanics

A general method to describe Hamiltonian chaos in the thermodynamic limit is presented which is based on a model equation independent of the dynamics. This equation is derived from a geometric approach to Hamiltonian chaos recently proposed, and provides an analytic estimate of the largest Lyapunov exponent $\ensuremath{\lambda}$. The particular case of the Fermi-Pasta-Ulam $\ensuremath{\beta}$-model Hamiltonian is considered, showing an excellent agreement between the values of $\ensuremath{\lambda}$ predicted by the model and those obtained with computer simulations of the tangent dynamics.