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arXiv · 1605.08765

On the recurrence and Lyapunov time scales of the motion near the chaos border

Ivan I. Shevchenko
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Abstract

Conditions for the emergence of a statistical relationship between $T_r$, the chaotic transport (recurrence) time, and $T_L$, the local Lyapunov time (the inverse of the numerically measured largest Lyapunov characteristic exponent), are considered for the motion inside the chaotic layer around the separatrix of a nonlinear resonance. When numerical values of the Lyapunov exponents are measured on a time interval not greater than $T_r$, the relationship is shown to resemble the quadratic one. This tentatively explains numerical results presented in the literature.

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Ivan I. Shevchenko. 2016-05-27. On the recurrence and Lyapunov time scales of the motion near the chaos border. https://doi.org/10.1016/s0375-9601(98)00093-0

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