Lyapunov time
E181628
Lyapunov time is a measure in dynamical systems theory that quantifies how long it takes for small differences in initial conditions to grow exponentially and significantly affect a system’s future behavior, indicating the timescale of predictability.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Lyapunov time canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1597825 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lyapunov time Context triple: [Aleksandr Lyapunov, notableConcept, Lyapunov time]
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A.
Laplace resonance
Laplace resonance is a three-body orbital resonance in which the orbital periods of Jupiter’s moons Io, Europa, and Ganymede are linked in a precise 1:2:4 ratio, strongly affecting their dynamics and internal heating.
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B.
Poincaré recurrence theorem
The Poincaré recurrence theorem is a fundamental result in dynamical systems and ergodic theory stating that certain systems will, after a sufficiently long but finite time, return arbitrarily close to their initial state.
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C.
Planck time
Planck time is the fundamental unit of time in the system of Planck units, representing the shortest meaningful interval of time according to current physical theories, where quantum effects of gravity become significant.
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D.
Saros cycle
The Saros cycle is an approximately 18-year period after which nearly identical solar and lunar eclipses repeat, due to the alignment of the Earth, Moon, and Sun.
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E.
Milanković calendar
The Milanković calendar is a 20th-century reform of the Julian calendar, designed by Serbian scientist Milutin Milanković to more accurately align the civil year with the solar year and used by some Eastern Orthodox churches.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Lyapunov time Target entity description: Lyapunov time is a measure in dynamical systems theory that quantifies how long it takes for small differences in initial conditions to grow exponentially and significantly affect a system’s future behavior, indicating the timescale of predictability.
-
A.
Laplace resonance
Laplace resonance is a three-body orbital resonance in which the orbital periods of Jupiter’s moons Io, Europa, and Ganymede are linked in a precise 1:2:4 ratio, strongly affecting their dynamics and internal heating.
-
B.
Poincaré recurrence theorem
The Poincaré recurrence theorem is a fundamental result in dynamical systems and ergodic theory stating that certain systems will, after a sufficiently long but finite time, return arbitrarily close to their initial state.
-
C.
Planck time
Planck time is the fundamental unit of time in the system of Planck units, representing the shortest meaningful interval of time according to current physical theories, where quantum effects of gravity become significant.
-
D.
Saros cycle
The Saros cycle is an approximately 18-year period after which nearly identical solar and lunar eclipses repeat, due to the alignment of the Earth, Moon, and Sun.
-
E.
Milanković calendar
The Milanković calendar is a 20th-century reform of the Julian calendar, designed by Serbian scientist Milutin Milanković to more accurately align the civil year with the solar year and used by some Eastern Orthodox churches.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
concept in dynamical systems theory
ⓘ
measure of predictability ⓘ time scale ⓘ |
| appliesTo |
chaotic systems
ⓘ
deterministic dynamical systems ⓘ |
| associatedWith | exponential error growth ⓘ |
| assumes | positive largest Lyapunov exponent for chaos ⓘ |
| category |
Chaos theory
ⓘ
Dynamical systems ⓘ Mathematical physics ⓘ Nonlinear dynamics ⓘ |
| characterizes | rate of exponential divergence of nearby trajectories ⓘ |
| definedAs | inverse of the largest Lyapunov exponent ⓘ |
| dependsOn |
phase space structure
ⓘ
system dynamics ⓘ |
| hasUnit | time ⓘ |
| helpsDescribe | limits of long-term prediction ⓘ |
| indicates | horizon of reliable prediction ⓘ |
| isDifferentFrom |
correlation time
ⓘ
mixing time ⓘ physical relaxation time ⓘ |
| isFiniteWhen | system is chaotic ⓘ |
| isPropertyOf |
orbits in phase space
ⓘ
trajectories of dynamical systems ⓘ |
| longLyapunovTimeIndicates | greater predictability ⓘ |
| mathematicallyExpressedAs | T_L = 1 / λ_max ⓘ |
| namedAfter | Aleksandr Lyapunov ⓘ |
| quantifies |
time for small initial differences to grow significantly
ⓘ
time scale of predictability ⓘ |
| relatedTo |
Lyapunov exponents
ⓘ
surface form:
Lyapunov exponent
|
| shortLyapunovTimeIndicates | high sensitivity to initial conditions ⓘ |
| tendsToInfinityWhen | largest Lyapunov exponent is zero or negative ⓘ |
| usedIn |
N-body simulations
ⓘ
celestial mechanics ⓘ chaos theory ⓘ climate modeling ⓘ control of chaotic systems ⓘ dynamical systems ⓘ nonlinear dynamics ⓘ study of Solar System stability ⓘ weather forecasting ⓘ |
| usedTo |
assess stability of motion
ⓘ
compare predictability of different systems ⓘ estimate forecast horizon ⓘ |
| where | λ_max is the largest Lyapunov exponent ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Lyapunov time Description of subject: Lyapunov time is a measure in dynamical systems theory that quantifies how long it takes for small differences in initial conditions to grow exponentially and significantly affect a system’s future behavior, indicating the timescale of predictability.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.