mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, the Lyapunov time is the characteristic timescale on which a

dynamical system In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water i ...

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. It is named after the

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mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

Aleksandr Lyapunov. It is defined as the inverse of a system's largest

Lyapunov exponent In mathematics, the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectory, trajectories. Quantitatively, two trajectories in phase sp ...

Use

The Lyapunov time mirrors the limits of the

predictability Predictability is the degree to which a correct prediction or forecast of a system's state can be made, either qualitatively or quantitatively. Predictability and causality Causal determinism has a strong relationship with predictability. Per ...

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

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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:Pierre Gaspard, ''Chaos, Scattering and Statistical Mechanics'', Cambridge University Press, 2005. p. 7

References

{{reflist Dynamical systems

Use

Examples

See also

References