Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Stability_theory> ?p ?o. }
Showing items 1 to 35 of
35
with 100 items per page.
- Stability_theory abstract "In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. More generally, a theorem is stable if small changes in the hypothesis lead to small variations in the conclusion. One must specifythe metric used to measure the perturbations when claiming a theorem is stable. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while indifferential geometry one may measure the distance between spaces using the Gromov-Hausdorff distance. In dynamical systems, an orbit is called Lyapunov stable if the forward orbit of any point is in a small enough neighborhood or it stays in a small (but perhaps, larger) neighborhood. Various criteria have been developed to prove stability or instability of an orbit. Under favorable circumstances, the question may be reduced to a well-studied problem involving eigenvalues of matrices. A more general method involves Lyapunov functions. In practice, any one of a number of different stability criteria are applied.".
- Stability_theory wikiPageExternalLink StableEquilibria.
- Stability_theory wikiPageID "5493795".
- Stability_theory wikiPageRevisionID "583616259".
- Stability_theory curator "Philip Holmes and Eric T. Shea-Brown".
- Stability_theory hasPhotoCollection Stability_theory.
- Stability_theory title "Stability".
- Stability_theory urlname "Stability".
- Stability_theory subject Category:Limit_sets.
- Stability_theory subject Category:Stability_theory.
- Stability_theory type Abstraction100002137.
- Stability_theory type Collection107951464.
- Stability_theory type Group100031264.
- Stability_theory type LimitSets.
- Stability_theory type Set107996689.
- Stability_theory comment "In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle.".
- Stability_theory label "Stability theory".
- Stability_theory label "Stabilitätstheorie".
- Stability_theory label "Stabilność układu automatycznej regulacji".
- Stability_theory label "Teoría de la estabilidad".
- Stability_theory label "Théorie de la stabilité".
- Stability_theory label "Теория устойчивости".
- Stability_theory label "نظرية الاستقرار".
- Stability_theory label "安定性理論".
- Stability_theory sameAs Stabilitätstheorie.
- Stability_theory sameAs Teoría_de_la_estabilidad.
- Stability_theory sameAs Théorie_de_la_stabilité.
- Stability_theory sameAs 安定性理論.
- Stability_theory sameAs Stabilność_układu_automatycznej_regulacji.
- Stability_theory sameAs m.0dp8wj.
- Stability_theory sameAs Q1756677.
- Stability_theory sameAs Q1756677.
- Stability_theory sameAs Stability_theory.
- Stability_theory wasDerivedFrom Stability_theory?oldid=583616259.
- Stability_theory isPrimaryTopicOf Stability_theory.