Pesin theory
E695941
Pesin theory is a branch of dynamical systems that studies the statistical and geometric behavior of non-uniformly hyperbolic systems, particularly through the use of Lyapunov exponents and invariant manifolds.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Pesin theory canonical | 5 |
How this entity was disambiguated
This entity first appeared as the object of triple T7833159 — 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: Pesin theory Context triple: [Lyapunov exponents, relatedTo, Pesin theory]
-
A.
Milnor–Thurston kneading theory
Milnor–Thurston kneading theory is a mathematical framework in one-dimensional dynamical systems that encodes the combinatorial behavior of interval maps to study their dynamics and entropy.
-
B.
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.
-
C.
Page theorem
The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
-
D.
Oblique Function theory
Oblique Function theory is an architectural concept developed by Claude Parent (often with Paul Virilio) that advocates sloping, inclined planes in buildings to disrupt traditional vertical-horizontal spatial organization and transform how people move and inhabit space.
-
E.
Khinchin–Kolmogorov theorem
The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
- 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: Pesin theory Target entity description: Pesin theory is a branch of dynamical systems that studies the statistical and geometric behavior of non-uniformly hyperbolic systems, particularly through the use of Lyapunov exponents and invariant manifolds.
-
A.
Milnor–Thurston kneading theory
Milnor–Thurston kneading theory is a mathematical framework in one-dimensional dynamical systems that encodes the combinatorial behavior of interval maps to study their dynamics and entropy.
-
B.
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.
-
C.
Page theorem
The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
-
D.
Oblique Function theory
Oblique Function theory is an architectural concept developed by Claude Parent (often with Paul Virilio) that advocates sloping, inclined planes in buildings to disrupt traditional vertical-horizontal spatial organization and transform how people move and inhabit space.
-
E.
Khinchin–Kolmogorov theorem
The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
branch of dynamical systems theory
ⓘ
mathematical theory ⓘ |
| aimsToExplain | how non-uniform hyperbolicity yields ergodic and statistical properties ⓘ |
| appliesTo |
diffeomorphisms of smooth manifolds
ⓘ
flows on smooth manifolds ⓘ systems with non-zero Lyapunov exponents almost everywhere ⓘ |
| assumes |
differentiability conditions on the map
ⓘ
invariant probability measure ⓘ |
| concerns | almost-everywhere behavior with respect to an invariant measure ⓘ |
| developedBy | Yakov Pesin ⓘ |
| developedIn | 1970s ⓘ |
| fieldOfStudy |
non-uniformly hyperbolic dynamical systems
ⓘ
smooth dynamical systems ⓘ |
| frameworkFor | studying chaotic behavior in smooth systems ⓘ |
| generalizes | hyperbolic theory of dynamical systems ⓘ |
| hasApplicationIn |
differentiable dynamical systems
ⓘ
smooth chaotic dynamics ⓘ statistical properties of chaotic systems ⓘ |
| hasKeyResult |
Pesin entropy formula
ⓘ
linked to:
Kolmogorov–Sinai entropy
absolute continuity of stable and unstable foliations ⓘ existence of stable and unstable manifolds for almost every point ⓘ non-uniform hyperbolicity implies strong statistical properties ⓘ |
| influenced |
modern smooth ergodic theory
ⓘ
research on SRB measures and physical measures ⓘ |
| relatedTo |
Anosov systems
ⓘ
Oseledets multiplicative ergodic theorem ⓘ
linked to:
Oseledets theorem
Sinai–Ruelle–Bowen measures ⓘ
linked to:
Sinai–Ruelle–Bowen measure
partial hyperbolicity ⓘ smooth ergodic theory ⓘ uniformly hyperbolic theory ⓘ |
| studiesProperty |
Lyapunov spectrum
ⓘ
Oseledets splitting ⓘ SRB measures ⓘ absolutely continuous invariant measures ⓘ geometric behavior of dynamical systems ⓘ metric entropy ⓘ non-uniform expansion and contraction rates ⓘ orbit structure ⓘ stable and unstable manifolds ⓘ statistical behavior of dynamical systems ⓘ |
| usesConcept |
Lyapunov exponents
ⓘ
ergodic theory ⓘ hyperbolicity ⓘ invariant manifolds ⓘ measure theory ⓘ non-uniform hyperbolicity ⓘ |
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: Pesin theory Description of subject: Pesin theory is a branch of dynamical systems that studies the statistical and geometric behavior of non-uniformly hyperbolic systems, particularly through the use of Lyapunov exponents and invariant manifolds.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.