Lyapunov vector
E181626
A Lyapunov vector is a mathematical construct in dynamical systems theory that characterizes the directions in phase space associated with exponential growth or decay rates quantified by Lyapunov exponents.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Lyapunov vector canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T1597813 — 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 vector Context triple: [Aleksandr Lyapunov, notableWork, Lyapunov vector]
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A.
Onsager–Machlup function
The Onsager–Machlup function is a functional in stochastic process theory that characterizes the most probable paths of fluctuating systems, playing a key role in nonequilibrium statistical mechanics and large deviation theory.
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B.
Lie derivative
The Lie derivative is a fundamental differential operator in differential geometry that measures how a tensor field changes along the flow generated by a vector field.
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C.
Laplace operator
The Laplace operator is a second-order differential operator widely used in mathematics and physics to describe phenomena such as diffusion, heat flow, and wave propagation.
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D.
Ornstein–Uhlenbeck process
The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
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E.
Poynting vector
The Poynting vector is a fundamental quantity in electromagnetism that represents the directional energy flux (power per unit area) carried by an electromagnetic field.
- 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 vector Target entity description: A Lyapunov vector is a mathematical construct in dynamical systems theory that characterizes the directions in phase space associated with exponential growth or decay rates quantified by Lyapunov exponents.
-
A.
Onsager–Machlup function
The Onsager–Machlup function is a functional in stochastic process theory that characterizes the most probable paths of fluctuating systems, playing a key role in nonequilibrium statistical mechanics and large deviation theory.
-
B.
Lie derivative
The Lie derivative is a fundamental differential operator in differential geometry that measures how a tensor field changes along the flow generated by a vector field.
-
C.
Laplace operator
The Laplace operator is a second-order differential operator widely used in mathematics and physics to describe phenomena such as diffusion, heat flow, and wave propagation.
-
D.
Ornstein–Uhlenbeck process
The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
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E.
Poynting vector
The Poynting vector is a fundamental quantity in electromagnetism that represents the directional energy flux (power per unit area) carried by an electromagnetic field.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical concept
ⓘ
object in dynamical systems theory ⓘ |
| appliesTo |
continuous-time dynamical systems
ⓘ
discrete-time dynamical systems ⓘ |
| associatedWith |
linearized dynamics
ⓘ
tangent space of a trajectory ⓘ variational equations ⓘ |
| belongsTo | Oseledec splitting ⓘ |
| characterizes |
directions in phase space
ⓘ
directions of exponential decay ⓘ directions of exponential growth ⓘ |
| computedBy |
Benettin algorithm
ⓘ
QR-based methods ⓘ covariant Lyapunov vector algorithms ⓘ |
| correspondsTo | a particular Lyapunov exponent ⓘ |
| definedBy |
Lyapunov exponents
ⓘ
surface form:
Oseledec multiplicative ergodic theorem
|
| dependsOn |
choice of norm up to equivalence class
ⓘ
invariant measure of the system ⓘ |
| differsFrom | eigenvector of instantaneous Jacobian in general nonlinear systems ⓘ |
| forms | a basis adapted to the Lyapunov exponents ⓘ |
| hasProperty |
can be covariant
ⓘ
can be forward-time or backward-time ⓘ defined along a trajectory ⓘ time-dependent ⓘ |
| hasType |
backward Lyapunov vector
ⓘ
covariant Lyapunov vector ⓘ forward Lyapunov vector ⓘ |
| livesIn | tangent space ⓘ |
| namedAfter | Aleksandr Lyapunov ⓘ |
| quantifiedBy | Lyapunov exponents ⓘ |
| relatedTo |
Lyapunov exponents
ⓘ
surface form:
Lyapunov characteristic exponent
Lyapunov exponents ⓘ
surface form:
Lyapunov exponent
Lyapunov exponents ⓘ
surface form:
Lyapunov spectrum
eigenvectors of the Jacobian in linear systems ⓘ |
| studiedIn |
applied mathematics
ⓘ
ergodic theory ⓘ |
| usedFor |
characterizing chaotic attractors
ⓘ
hyperbolicity analysis ⓘ identifying stable directions ⓘ identifying unstable directions ⓘ mode decomposition in high-dimensional systems ⓘ predictability studies ⓘ sensitivity analysis ⓘ |
| usedIn |
chaos theory
ⓘ
dynamical systems ⓘ nonlinear dynamics ⓘ stability analysis ⓘ |
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 vector Description of subject: A Lyapunov vector is a mathematical construct in dynamical systems theory that characterizes the directions in phase space associated with exponential growth or decay rates quantified by Lyapunov exponents.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.