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.
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
NERFINISHED
ⓘ
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
NERFINISHED
ⓘ
Markov partitions NERFINISHED ⓘ 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 ⓘ |
Referenced by (1)
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