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arXiv · 1008.4708

Lyapunov exponent of the random frequency oscillator: cumulant expansion approach

C. Anteneodo·R. O. Vallejos
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Abstract

We consider a one-dimensional harmonic oscillator with a random frequency, focusing on both the standard and the generalized Lyapunov exponents, $λ$ and $λ^\star$ respectively. We discuss the numerical difficulties that arise in the numerical calculation of $λ^\star$ in the case of strong intermittency. When the frequency corresponds to a Ornstein-Uhlenbeck process, we compute analytically $λ^\star$ by using a cumulant expansion including up to the fourth order. Connections with the problem of finding an analytical estimate for the largest Lyapunov exponent of a many-body system with smooth interactions are discussed.

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C. Anteneodo, R. O. Vallejos. 2010-08-27. Lyapunov exponent of the random frequency oscillator: cumulant expansion approach. https://doi.org/10.1088/1742-6596%2F246%2F1%2F012002

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