Statements (54)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
diffeomorphism
|
| gptkbp:canEstablish |
sensitive dependence on initial conditions
bifurcation phenomena |
| gptkbp:exhibits |
hyperbolic behavior
|
| gptkbp:hasCapacity |
stable manifold
unstable manifold |
| gptkbp:hasExhibition |
dynamical system
|
| gptkbp:hasVariants |
Lebesgue measure
|
| https://www.w3.org/2000/01/rdf-schema#label |
Anosov diffeomorphism
|
| gptkbp:isA |
diffeomorphism with hyperbolic properties
dynamical system with hyperbolic structure example of a hyperbolic system smooth dynamical system smooth manifold mapping smooth map topological dynamical system dynamical system with stable and unstable manifolds |
| gptkbp:isAvenueFor |
chaos theory
|
| gptkbp:isCharacterizedBy |
Lyapunov stability
differentiable dynamics differentiable structure existence of invariant sets existence of stable and unstable manifolds expanding and contracting directions exponential divergence of trajectories exponential growth rates uniform_hyperbolicity |
| gptkbp:isConnectedTo |
topological entropy
|
| gptkbp:isCounteredBy |
differential equations
|
| gptkbp:isDescribedAs |
manifold
|
| gptkbp:isNamedAfter |
gptkb:Dmitri_Anosov
|
| gptkbp:isRelatedTo |
mathematical modeling
nonlinear dynamics Lyapunov exponents chaotic behavior dynamical systems theory Poincaré recurrence theorem dynamical stability smooth dynamical systems |
| gptkbp:isStudiedIn |
theoretical physics
mathematics mathematical analysis topology ergodic theory differential topology |
| gptkbp:isUsedBy |
complex systems
|
| gptkbp:isUsedFor |
Anosov_system
|
| gptkbp:isUsedIn |
mathematical physics
computational mathematics statistical mechanics control theory dynamical systems geometric topology theory of dynamical systems |