Oseledec splitting
E695945
Oseledec splitting is a mathematical decomposition of a dynamical system’s tangent space into invariant subspaces associated with distinct Lyapunov exponents, characterizing the system’s asymptotic stability properties.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Oseledec splitting canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7833302 — 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: Oseledec splitting Context triple: [Lyapunov vector, belongsTo, Oseledec splitting]
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A.
Lyapunov exponents
Lyapunov exponents are quantitative measures in dynamical systems theory that characterize the rates at which nearby trajectories diverge or converge, indicating the presence and strength of chaos.
-
B.
Sylvester’s law of inertia
Sylvester’s law of inertia is a theorem in linear algebra stating that the numbers of positive, negative, and zero eigenvalues (the inertia) of a real symmetric matrix are invariant under change of basis.
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C.
May–Wigner stability theorem
The May–Wigner stability theorem is a result in theoretical ecology and random matrix theory showing that large, complex systems with many random interactions are generically unstable beyond a critical level of complexity.
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D.
Kakutani equivalence in ergodic theory
Kakutani equivalence in ergodic theory is a notion of equivalence between measure-preserving dynamical systems based on the isomorphism of their induced transformations on subsets of positive measure.
-
E.
Young tower construction in nonuniformly hyperbolic dynamics
"Young tower construction in nonuniformly hyperbolic dynamics" is a foundational work in dynamical systems that introduced a powerful tower-based method for analyzing statistical properties such as decay of correlations and limit theorems in nonuniformly hyperbolic systems.
- 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: Oseledec splitting Target entity description: Oseledec splitting is a mathematical decomposition of a dynamical system’s tangent space into invariant subspaces associated with distinct Lyapunov exponents, characterizing the system’s asymptotic stability properties.
-
A.
Lyapunov exponents
Lyapunov exponents are quantitative measures in dynamical systems theory that characterize the rates at which nearby trajectories diverge or converge, indicating the presence and strength of chaos.
-
B.
Sylvester’s law of inertia
Sylvester’s law of inertia is a theorem in linear algebra stating that the numbers of positive, negative, and zero eigenvalues (the inertia) of a real symmetric matrix are invariant under change of basis.
-
C.
May–Wigner stability theorem
The May–Wigner stability theorem is a result in theoretical ecology and random matrix theory showing that large, complex systems with many random interactions are generically unstable beyond a critical level of complexity.
-
D.
Kakutani equivalence in ergodic theory
Kakutani equivalence in ergodic theory is a notion of equivalence between measure-preserving dynamical systems based on the isomorphism of their induced transformations on subsets of positive measure.
-
E.
Young tower construction in nonuniformly hyperbolic dynamics
"Young tower construction in nonuniformly hyperbolic dynamics" is a foundational work in dynamical systems that introduced a powerful tower-based method for analyzing statistical properties such as decay of correlations and limit theorems in nonuniformly hyperbolic systems.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
invariant splitting
ⓘ
mathematical concept ⓘ structure in dynamical systems ⓘ |
| appliesTo |
differentiable dynamical systems
ⓘ
linear cocycles ⓘ random dynamical systems ⓘ |
| associates | invariant subspaces to Lyapunov exponents ⓘ |
| assumes | integrability conditions on the derivative cocycle ⓘ |
| basedOn | multiplicative ergodic theorem NERFINISHED ⓘ |
| characterizes |
asymptotic growth rates of tangent vectors
ⓘ
asymptotic stability properties ⓘ |
| context |
ergodic measure-preserving transformations
ⓘ
measure-preserving dynamical systems ⓘ |
| decomposes | tangent space ⓘ |
| describes |
decomposition into Oseledec subspaces
ⓘ
directions with distinct exponential growth rates ⓘ |
| domain | tangent bundle of a dynamical system ⓘ |
| field |
dynamical systems
ⓘ
ergodic theory ⓘ smooth dynamical systems ⓘ |
| generalizationOf | spectral decomposition for products of random matrices ⓘ |
| implies | existence of Lyapunov exponents almost everywhere ⓘ |
| mathematicalArea |
applied mathematics
ⓘ
differential geometry ⓘ probability theory ⓘ |
| namedAfter | Vladimir Oseledets NERFINISHED ⓘ |
| property |
defined almost everywhere with respect to an invariant measure
ⓘ
invariance under the derivative cocycle ⓘ measurability with respect to the invariant measure ⓘ uniqueness up to sets of measure zero ⓘ |
| relatedTo |
Lyapunov exponents
NERFINISHED
ⓘ
Lyapunov spectrum NERFINISHED ⓘ Oseledec theorem NERFINISHED ⓘ center subspaces ⓘ cocycles over dynamical systems ⓘ dominated splittings ⓘ hyperbolic dynamics ⓘ invariant measures ⓘ random matrix products ⓘ stable subspaces ⓘ unstable subspaces ⓘ |
| usedFor |
Pesin theory
NERFINISHED
ⓘ
characterization of stable and unstable directions ⓘ numerical computation of Lyapunov exponents ⓘ study of nonuniform hyperbolicity ⓘ |
| usedIn | the study of chaotic dynamical systems ⓘ |
| yields | filtration of the tangent space by Lyapunov exponents ⓘ |
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: Oseledec splitting Description of subject: Oseledec splitting is a mathematical decomposition of a dynamical system’s tangent space into invariant subspaces associated with distinct Lyapunov exponents, characterizing the system’s asymptotic stability properties.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.