Local chaotic behaviour in the Fermi-Pasta-Ulam system

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November 2005, 5(4): 991-1004. doi: 10.3934/dcdsb.2005.5.991

Local chaotic behaviour in the Fermi-Pasta-Ulam system

Antonio Giorgilli ^1, , Simone Paleari ^1, and Tiziano Penati ^1,

1.	Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via R. Cozzi 53, 20125 - Milano, Italy, Italy, Italy

Received November 2004 Revised April 2005 Published August 2005

Abstract
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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 different 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.

Keywords: Nonlinear chain, Thermodynamic limit., FPU model.

Mathematics Subject Classification: Primary: 34C15, 70K55; Secondary: 34C2.

Citation: Antonio Giorgilli, Simone Paleari, Tiziano Penati. Local chaotic behaviour in the Fermi-Pasta-Ulam system. Discrete & Continuous Dynamical Systems - B, 2005, 5 (4) : 991-1004. doi: 10.3934/dcdsb.2005.5.991

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