Lyapunov time
Encyclopedia
In mathematics
, the Lyapunov time is the length of time for a dynamical system
to become chaotic
. 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
.
It is named after the Russia
n mathematician
Aleksandr Lyapunov
who died in 1918.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the Lyapunov time is the length of time for a dynamical system
Dynamical system
A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a...
to become chaotic
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...
. The Lyapunov time reflects the limits of the predictability
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:...
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
E (mathematical constant)
The mathematical constant ' is the unique real number such that the value of the derivative of the function at the point is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base...
.
It is named after the Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
Aleksandr Lyapunov
Aleksandr Lyapunov
Aleksandr Mikhailovich Lyapunov was a Russian mathematician, mechanician and physicist. His surname is sometimes romanized as Ljapunov, Liapunov or Ljapunow....
who died in 1918.