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.
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 ⓘ |
Referenced by (1)
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