• Source: Lyapunov time

In mathematics, the Lyapunov time is the characteristic timescale on which a dynamical system is chaotic. It is named after the Russian mathematician Aleksandr Lyapunov. It is defined as the inverse of a system's largest Lyapunov exponent.




Use


The Lyapunov time mirrors the limits of the predictability of the system. By convention, it is defined as the time for the distance between nearby trajectories of the system to increase by a factor of e. However, measures in terms of 2-foldings and 10-foldings are sometimes found, since they correspond to the loss of one bit of information or one digit of precision respectively.
While it is used in many applications of dynamical systems theory, it has been particularly used in celestial mechanics where it is important for the problem of the stability of the Solar System. However, empirical estimation of the Lyapunov time is often associated with computational or inherent uncertainties.




Examples


Typical values are:




See also


Belousov–Zhabotinsky reaction
Molecular chaos
Three-body problem




References

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• Lyapunov time
• Lyapunov
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• Lyapunov exponent
• Lyapunov stability
• Lyapunov equation
• Lyapunov function
• Lyapunov theorem
• Chaos theory
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