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.
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 NERFINISHED ⓘ |
| 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
NERFINISHED
ⓘ
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
NERFINISHED
ⓘ
Oseledets multiplicative ergodic theorem NERFINISHED ⓘ Sinai–Ruelle–Bowen measures NERFINISHED ⓘ 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
NERFINISHED
ⓘ
ergodic theory ⓘ hyperbolicity ⓘ invariant manifolds ⓘ measure theory ⓘ non-uniform hyperbolicity ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.