Saturday, April 23, 2016

Lyapunov time and exponent

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. See the extensive discussion of the Lyapunov exponent, its inverse.


The Lyapunov time reflects 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 stability of the Solar System question. However, empirical estimation of the Lyapunov time is often associated with computational or inherent uncertainties

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Lyapunov Exponent

This is the inverse of Lyampunov time – see this link for a detailed explanation: 

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