Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
continuous dynamical systems
discrete dynamical systems smooth dynamical systems |
| gptkbp:describes |
existence of stable and unstable manifolds near hyperbolic fixed points
|
| gptkbp:field |
dynamical systems
partial differential equations |
| gptkbp:generalizes |
Lyapunov stability theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Stable Manifold Theorem
|
| gptkbp:provenBy |
gptkb:Hadamard
gptkb:Poincaré gptkb:Lyapunov |
| gptkbp:publishedIn |
Annales de l'École Normale Supérieure
|
| gptkbp:relatedTo |
hyperbolic fixed point
Hartman-Grobman Theorem |
| gptkbp:state |
there exists a local unstable manifold tangent to the unstable eigenspace at a hyperbolic fixed point
there exists a local stable manifold tangent to the stable eigenspace at a hyperbolic fixed point |
| gptkbp:usedIn |
chaos theory
bifurcation theory study of local behavior near equilibria |
| gptkbp:year |
1901
|
| gptkbp:bfsParent |
gptkb:hyperbolic_dynamical_systems
|
| gptkbp:bfsLayer |
7
|