Young tower construction in nonuniformly hyperbolic dynamics
E621129
"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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Young tower construction in nonuniformly hyperbolic dynamics canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6834274 — 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: Young tower construction in nonuniformly hyperbolic dynamics Context triple: [Lai-Sang Young, notableWork, Young tower construction in nonuniformly hyperbolic dynamics]
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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.
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B.
Thurston’s classification of surface diffeomorphisms
Thurston’s classification of surface diffeomorphisms is a foundational theorem in low-dimensional topology that categorizes self-maps of surfaces into periodic, reducible, or pseudo-Anosov types, profoundly influencing the study of 3-manifolds and dynamical systems.
-
C.
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.
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D.
Sullivan dictionary relating Kleinian groups and complex dynamics
The Sullivan dictionary relating Kleinian groups and complex dynamics is a conceptual framework that draws deep analogies between the theory of Kleinian groups and the iteration of rational maps, unifying key ideas in geometric group theory and complex dynamical systems.
-
E.
Lectures on Ergodic Theory
"Lectures on Ergodic Theory" is a classic mathematical monograph that systematically develops the foundations and key results of ergodic theory within dynamical 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: Young tower construction in nonuniformly hyperbolic dynamics Target entity description: "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.
-
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.
Thurston’s classification of surface diffeomorphisms
Thurston’s classification of surface diffeomorphisms is a foundational theorem in low-dimensional topology that categorizes self-maps of surfaces into periodic, reducible, or pseudo-Anosov types, profoundly influencing the study of 3-manifolds and dynamical systems.
-
C.
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.
-
D.
Sullivan dictionary relating Kleinian groups and complex dynamics
The Sullivan dictionary relating Kleinian groups and complex dynamics is a conceptual framework that draws deep analogies between the theory of Kleinian groups and the iteration of rational maps, unifying key ideas in geometric group theory and complex dynamical systems.
-
E.
Lectures on Ergodic Theory
"Lectures on Ergodic Theory" is a classic mathematical monograph that systematically develops the foundations and key results of ergodic theory within dynamical systems.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
construction in dynamical systems
ⓘ
mathematical method ⓘ tool in ergodic theory ⓘ |
| appliesTo |
Hénon-like maps
ⓘ
billiard systems ⓘ intermittent maps ⓘ nonuniformly expanding maps ⓘ nonuniformly hyperbolic maps ⓘ partially hyperbolic systems ⓘ |
| assumes |
absolute continuity of stable and unstable foliations
ⓘ
bounded distortion along unstable manifolds ⓘ nonuniform hyperbolicity along stable and unstable directions ⓘ |
| basedOn |
Markov extensions
ⓘ
linked to:
Markov partition
hyperbolic product structure ⓘ inducing schemes ⓘ |
| characterizedBy |
Gibbs-like properties of reference measures
ⓘ
Markov structure on the tower ⓘ return time function to the base ⓘ tower with base and levels ⓘ |
| enables |
reduction of dynamics to a symbolic model
ⓘ
spectral analysis of the Perron–Frobenius operator ⓘ use of transfer operator techniques ⓘ |
| field |
dynamical systems
ⓘ
ergodic theory ⓘ nonuniformly hyperbolic dynamics ⓘ |
| implies |
exponential decay of correlations under exponential tail conditions
ⓘ
polynomial decay of correlations under polynomial tail conditions ⓘ |
| influenced |
applications to smooth ergodic theory
ⓘ
modern theory of statistical properties of dynamical systems ⓘ research on decay of correlations in nonuniformly hyperbolic systems ⓘ |
| notableFor |
providing a unified framework for many nonuniformly hyperbolic examples
ⓘ
yielding sharp statistical estimates from geometric assumptions ⓘ |
| relatedTo |
Gibbs–Markov maps
ⓘ
Markov partitions ⓘ
linked to:
Markov partition
Young towers ⓘ induced Markov maps ⓘ |
| usedFor |
analyzing invariant measures
ⓘ
deriving central limit theorems ⓘ establishing limit theorems ⓘ proving almost sure invariance principles ⓘ proving decay of correlations ⓘ studying SRB measures ⓘ studying large deviations ⓘ studying statistical properties of dynamical systems ⓘ |
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: Young tower construction in nonuniformly hyperbolic dynamics Description of subject: "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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.