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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.".
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- Structural_stability wikiPageRevisionID "618899008".
- Structural_stability wikiPageWikiLink Aleksandr_Andronov.
- Structural_stability wikiPageWikiLink Aleksandr_Lyapunov.
- Structural_stability wikiPageWikiLink Andronov–Pontryagin_criterion.
- Structural_stability wikiPageWikiLink Anosov_diffeomorphism.
- Structural_stability wikiPageWikiLink Arnaud_Denjoy.
- Structural_stability wikiPageWikiLink Arnold_tongue.
- Structural_stability wikiPageWikiLink Arnolds_cat_map.
- Structural_stability wikiPageWikiLink Attractor.
- Structural_stability wikiPageWikiLink Boundary_(topology).
- Structural_stability wikiPageWikiLink Category:Differential_equations.
- Structural_stability wikiPageWikiLink Category:Dynamical_systems.
- Structural_stability wikiPageWikiLink Category:Stability_theory.
- Structural_stability wikiPageWikiLink Celestial_mechanics.
- Structural_stability wikiPageWikiLink Circle.
- Structural_stability wikiPageWikiLink Circle_map.
- Structural_stability wikiPageWikiLink Compact_set.
- Structural_stability wikiPageWikiLink Compact_space.
- Structural_stability wikiPageWikiLink Continuously_differentiable.
- Structural_stability wikiPageWikiLink Denjoy_theorem.
- Structural_stability wikiPageWikiLink Dense_set.
- Structural_stability wikiPageWikiLink Diffeomorphism.
- Structural_stability wikiPageWikiLink Differentiable_function.
- Structural_stability wikiPageWikiLink Differentiable_manifold.
- Structural_stability wikiPageWikiLink Dmitri_Anosov.
- Structural_stability wikiPageWikiLink Dynamical_system.
- Structural_stability wikiPageWikiLink Fixed_point_(mathematics).
- Structural_stability wikiPageWikiLink Flow_(mathematics).
- Structural_stability wikiPageWikiLink George_Birkhoff.
- Structural_stability wikiPageWikiLink George_David_Birkhoff.
- Structural_stability wikiPageWikiLink Hadamard_billiards.
- Structural_stability wikiPageWikiLink Hadamards_dynamical_system.
- Structural_stability wikiPageWikiLink Hassler_Whitney.
- Structural_stability wikiPageWikiLink Henri_Poincaré.
- Structural_stability wikiPageWikiLink Homeomorphism.
- Structural_stability wikiPageWikiLink Homeostasis.
- Structural_stability wikiPageWikiLink Homoclinic.
- Structural_stability wikiPageWikiLink Homoclinic_orbit.
- Structural_stability wikiPageWikiLink Hyperbolic_equilibrium_point.
- Structural_stability wikiPageWikiLink Jacobian_matrix_and_determinant.
- Structural_stability wikiPageWikiLink Lev_Pontryagin.
- Structural_stability wikiPageWikiLink Limit_cycle.
- Structural_stability wikiPageWikiLink Lyapunov_stability.
- Structural_stability wikiPageWikiLink Marston_Morse.
- Structural_stability wikiPageWikiLink Mathematics.
- Structural_stability wikiPageWikiLink Maurício_Peixoto.
- Structural_stability wikiPageWikiLink Metric_(mathematics).
- Structural_stability wikiPageWikiLink Morse–Smale_system.
- Structural_stability wikiPageWikiLink Non-wandering_set.
- Structural_stability wikiPageWikiLink Open_set.
- Structural_stability wikiPageWikiLink Ordinary_differential_equation.
- Structural_stability wikiPageWikiLink Oscillation.
- Structural_stability wikiPageWikiLink Peixotos_theorem.
- Structural_stability wikiPageWikiLink Periodic_orbit.
- Structural_stability wikiPageWikiLink Periodic_point.
- Structural_stability wikiPageWikiLink Poincaré_map.
- Structural_stability wikiPageWikiLink Poincaré_recurrence_map.
- Structural_stability wikiPageWikiLink René_Thom.
- Structural_stability wikiPageWikiLink Rotation_number.
- Structural_stability wikiPageWikiLink Self-stabilization.
- Structural_stability wikiPageWikiLink Singularity_theory.
- Structural_stability wikiPageWikiLink Smooth_manifold.
- Structural_stability wikiPageWikiLink Solomon_Lefschetz.
- Structural_stability wikiPageWikiLink Sphere.
- Structural_stability wikiPageWikiLink Stability_theory.
- Structural_stability wikiPageWikiLink Stephen_Smale.
- Structural_stability wikiPageWikiLink Strange_attractor.
- Structural_stability wikiPageWikiLink Superstabilization.
- Structural_stability wikiPageWikiLink Three-body_problem.
- Structural_stability wikiPageWikiLink Topological_conjugacy.
- Structural_stability wikiPageWikiLink Topologically_equivalent.
- Structural_stability wikiPageWikiLink Torus.
- Structural_stability wikiPageWikiLink Two-sphere.
- Structural_stability wikiPageWikiLink Vector_field.
- Structural_stability wikiPageWikiLink Wandering_set.
- Structural_stability wikiPageWikiLink Wikipedia:Citing_sources.
- Structural_stability wikiPageWikiLinkText "Structural stability".
- Structural_stability wikiPageWikiLinkText "robust".
- Structural_stability wikiPageWikiLinkText "stability".
- Structural_stability wikiPageWikiLinkText "stable".
- Structural_stability wikiPageWikiLinkText "structural stability".
- Structural_stability wikiPageWikiLinkText "structurally stable".
- 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 wikiPageUsesTemplate Template:Cite_journal.
- Structural_stability wikiPageUsesTemplate Template:Eom.
- Structural_stability wikiPageUsesTemplate Template:One_source.
- Structural_stability wikiPageUsesTemplate Template:Scholarpedia.
- Structural_stability subject Category:Differential_equations.