We discuss the use of the maximal Lyapunov Characteristic Number as a stochasticity indicator in connection with the persistence of the FPU paradox in the thermodynamic limit. We show that the positiveness of the LCN does not imply that the dynamic is ergodic in statistical sense. On the other hand, our numerical exploration suggests that the energy surface may be separated into di®erent chaotic regions that may trap the orbit for a long time. This is compatible with the existence of exponentially long times of relaxation to statistical equilibrium in the sense of Nekhoroshev's theory. Thus, the relevance of the FPU phenomenon for large systems remains a still open problem.

Local chaotic behaviour in the Fermi-Pasta-Ulam system / A. Giorgilli, S. Paleari, T. Penati. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.. - ISSN 1531-3492. - 5:4(2005), pp. 991-1004. [10.3934/dcdsb.2005.5.991]

Local chaotic behaviour in the Fermi-Pasta-Ulam system

A. Giorgilli
Primo
;
S. Paleari
Secondo
;
T. Penati
Ultimo
2005

Abstract

We discuss the use of the maximal Lyapunov Characteristic Number as a stochasticity indicator in connection with the persistence of the FPU paradox in the thermodynamic limit. We show that the positiveness of the LCN does not imply that the dynamic is ergodic in statistical sense. On the other hand, our numerical exploration suggests that the energy surface may be separated into di®erent chaotic regions that may trap the orbit for a long time. This is compatible with the existence of exponentially long times of relaxation to statistical equilibrium in the sense of Nekhoroshev's theory. Thus, the relevance of the FPU phenomenon for large systems remains a still open problem.
FPU model; Nonlinear chain; Thermodynamic limit
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/15143
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