### Abstract

The existence of the thermodynamic limit for the spectrum of the Lyapunov

characteristic exponents is numerically investigated for the Fermi-Pasta-Ulam p model. We show that the shape of the spectrum for energy density well above the equipartition threshold E, allows the Kolmogorov-Sinai entropy to be expressed simply in terms of the maximum exponent I,,,. The presence of a power-law behaviour E@ is investigated. The analogies with similar results obtained from the dynamics of symplectic random matrices seem to indicate the possibility of interpreting chaotic dynamics in terms of some 'universal' properties.

characteristic exponents is numerically investigated for the Fermi-Pasta-Ulam p model. We show that the shape of the spectrum for energy density well above the equipartition threshold E, allows the Kolmogorov-Sinai entropy to be expressed simply in terms of the maximum exponent I,,,. The presence of a power-law behaviour E@ is investigated. The analogies with similar results obtained from the dynamics of symplectic random matrices seem to indicate the possibility of interpreting chaotic dynamics in terms of some 'universal' properties.

Original language | English |
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Pages (from-to) | 2033-2040 |

Number of pages | 8 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 19 |

Issue number | 11 |

Publication status | Published - 1 Aug 1986 |

## Cite this

Livi, R., Politi, A., & Ruffo, S. (1986). Distribution of characteristic exponents in the thermodynamic limit.

*Journal of Physics A: Mathematical and General*,*19*(11), 2033-2040. http://iopscience.iop.org/0305-4470/19/11/012