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- Structural_stability abstract "In mathematics, structural stability is a fundamental property of a dynamical system which means that the qualitative behavior of the trajectories is unaffected by small perturbations (to be exact C1-small perturbations).Examples of such qualitative properties are numbers of fixed points and periodic orbits (but not their periods). Unlike Lyapunov stability, which considers perturbations of initial conditions for a fixed system, structural stability deals with perturbations of the system itself. Variants of this notion apply to systems of ordinary differential equations, vector fields on smooth manifolds and flows generated by them, and diffeomorphisms.Structurally stable systems were introduced by Aleksandr Andronov and Lev Pontryagin in 1937 under the name "systèmes grossiers", or rough systems. They announced a characterization of rough systems in the plane, the Andronov–Pontryagin criterion. In this case, structurally stable systems are typical, they form an open dense set in the space of all systems endowed with appropriate topology. In higher dimensions, this is no longer true, indicating that typical dynamics can be very complex (cf strange attractor). An important class of structurally stable systems in arbitrary dimensions is given by Anosov diffeomorphisms and flows.".
- Structural_stability wikiPageID "2515807".
- Structural_stability wikiPageRevisionID "601195963".
- Structural_stability author "D.V. Anosov".
- Structural_stability curator "Charles Pugh and Maurício Matos Peixoto".
- Structural_stability date "December 2010".
- Structural_stability hasPhotoCollection Structural_stability.
- Structural_stability id "r/r082720".
- Structural_stability text "This article lacks inline citations.".
- Structural_stability title "Rough system".
- Structural_stability title "Structural stability".
- Structural_stability urlname "Structural_stability".
- Structural_stability subject Category:Differential_equations.
- Structural_stability subject Category:Dynamical_systems.
- Structural_stability subject Category:Stability_theory.
- Structural_stability type Abstraction100002137.
- Structural_stability type Attribute100024264.
- Structural_stability type Communication100033020.
- Structural_stability type DifferentialEquation106670521.
- Structural_stability type DifferentialEquations.
- Structural_stability type DynamicalSystem106246361.
- Structural_stability type DynamicalSystems.
- Structural_stability type Equation106669864.
- Structural_stability type MathematicalStatement106732169.
- Structural_stability type Message106598915.
- Structural_stability type PhaseSpace100029114.
- Structural_stability type Space100028651.
- Structural_stability type Statement106722453.
- Structural_stability comment "In mathematics, structural stability is a fundamental property of a dynamical system which means that the qualitative behavior of the trajectories is unaffected by small perturbations (to be exact C1-small perturbations).Examples of such qualitative properties are numbers of fixed points and periodic orbits (but not their periods).".
- Structural_stability label "Estabilidade estrutural".
- Structural_stability label "Stabilità strutturale".
- Structural_stability label "Structural stability".
- Structural_stability label "Strukturelle Stabilität".
- Structural_stability label "Структурная устойчивость".
- Structural_stability label "استقرار بنيوي".
- Structural_stability label "構造安定".
- Structural_stability sameAs Strukturelle_Stabilität.
- Structural_stability sameAs Stabilità_strutturale.
- Structural_stability sameAs 構造安定.
- Structural_stability sameAs Estabilidade_estrutural.
- Structural_stability sameAs m.07k863.
- Structural_stability sameAs Q1648886.
- Structural_stability sameAs Q1648886.
- Structural_stability sameAs Structural_stability.
- Structural_stability wasDerivedFrom Structural_stability?oldid=601195963.
- Structural_stability isPrimaryTopicOf Structural_stability.