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.[1]
^Bezruchko, Boris P.; Smirnov, Dmitry A. (5 September 2010). Extracting Knowledge from Time Series: An Introduction to Nonlinear Empirical Modeling. Springer. pp. 56–57. ISBN 9783642126000.
Lyapunovtime is the characteristic timescale on which a dynamical system is chaotic. It is named after the Russian mathematician Aleksandr Lyapunov....
following are named: Lyapunov dimension Lyapunov equation Lyapunov exponent Lyapunov function Lyapunov fractal Lyapunov stability Lyapunov's central limit theorem...
In mathematics, the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation...
theory of ordinary differential equations (ODEs), Lyapunov functions, named after Aleksandr Lyapunov, are scalar functions that may be used to prove the...
stability (ISS) applies Lyapunov notions to systems with inputs. Lyapunov stability is named after Aleksandr Mikhailovich Lyapunov, a Russian mathematician...
Lyapunov theorem may refer to: Lyapunov theory, a theorem related to the stability of solutions of differential equations near a point of equilibrium...
The Lyapunov equation, named after the Russian mathematician Aleksandr Lyapunov, is a matrix equation used in the stability analysis of linear dynamical...
can be measured, and a time scale depending on the dynamics of the system, called the Lyapunovtime. Some examples of Lyapunov times are: chaotic electrical...
_{t_{0}}^{t_{1}}})/(t_{1}-t_{0})} , which is then precisely the finite-timeLyapunov exponent (FTLE) F T L E t 0 t 1 ( x 0 ) = 1 2 ( t 1 − t 0 ) log λ...
million years (both forward and backward in time), but after intervals much longer than the Lyapunovtime of 10–20 million years, calculations become...
unpredictable given initial conditions. This includes Cauchy horizon Lyapunov exponent Lyapunovtime Butterfly effect This disambiguation page lists articles associated...
Pluto with any degree of accuracy more than 10–20 million years (the Lyapunovtime) into the future. Another example is Earth's axial tilt, which, due...
Ergodic hypothesis Ergodic process Kruskal principle Lindy effect Lyapunovtime – the time limit to the predictability of the system Maximal ergodic theorem...
planets' orbits are chaotic over longer time scales, in such a way that the whole Solar System possesses a Lyapunovtime in the range of 2~230 million years...
the rate of growth of these moments is limited by the Lyapunov condition given below. Lyapunov CLT — Suppose { X 1 , … , X n , … } {\textstyle \{X_{1}...
In the mathematics of dynamical systems, the concept of Lyapunov dimension was suggested by Kaplan and Yorke for estimating the Hausdorff dimension of...
The Lyapunov family (Russian: Ляпуно́в) is a Russian noble family claiming descent from the Galich Rurikids, who lost their princely title in the 15th...
article describes Lyapunov optimization for dynamical systems. It gives an example application to optimal control in queueing networks. Lyapunov optimization...
Aleksandr Lyapunov, founder of stability theory, author of the Lyapunov's central limit theorem, Lyapunov equation, Lyapunov fractal, Lyapunovtime etc. Leonty...
computed Lyapunovtime for this asteroid is only 6,000 years, indicating that it occupies a chaotic orbit that will change randomly over time because of...
computed Lyapunovtime for this asteroid is only 4,000 years, indicating that it occupies a highly chaotic orbit that will change randomly over time because...
Recurrence quantification analysis Lyapunov exponents Entropy encoding Time-series metrics or features that can be used for time series classification or regression...
predictions of its location progressively inaccurate over time. Estimates in 1993 put the Lyapunovtime horizon for predictability at around 50 years, after...
Aleksandr Lyapunov, founder of stability theory, author of the Lyapunov's central limit theorem, Lyapunov equation, Lyapunov fractal, Lyapunovtime Leonty...
these dates are in a uniform time scale such as Terrestrial Time. When converted to our ordinary solar time or Universal Time, which is decidedly non-uniform...
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