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- Center_manifold abstract "In mathematics, the center manifold of an equilibrium point of a dynamical system consists of orbits whose behavior around the equilibrium point is not controlled by either the attraction of the stable manifold or the repulsion of the unstable manifold. The first step when studying equilibrium points of dynamical systems is to linearize the system. The eigenvectors corresponding to eigenvalues with negative real part form the stable eigenspace, which gives rise to the stable manifold. Similarly, eigenvalues with positive real part yield the unstable manifold.This concludes the story if the equilibrium point is hyperbolic (i.e., all eigenvalues of the linearization have nonzero real part). However, if there are eigenvalues whose real part is zero, then these give rise to the center manifold. If the eigenvalues are precisely zero, rather than just real part being zero, then these more specifically give rise to a slow manifold. The behavior on the center (slow) manifold is generally not determined by the linearization and thus is more difficult to study.Center manifolds play an important role in: bifurcation theory because interesting behavior takes place on the center manifold; and multiscale mathematics because the long time dynamics often are attracted to a relatively simple center manifold.".
- Center_manifold thumbnail Saddle-node_phase_portrait_with_central_manifold.svg?width=300.
- Center_manifold wikiPageExternalLink gencm.php.
- Center_manifold wikiPageExternalLink sdenf.php.
- Center_manifold wikiPageExternalLink sdesm.php.
- Center_manifold wikiPageID "3948656".
- Center_manifold wikiPageLength "12550".
- Center_manifold wikiPageOutDegree "31".
- Center_manifold wikiPageRevisionID "663129198".
- Center_manifold wikiPageWikiLink Bifurcation_theory.
- Center_manifold wikiPageWikiLink Canonical_form.
- Center_manifold wikiPageWikiLink Category:Dynamical_systems.
- Center_manifold wikiPageWikiLink Center_manifold_reduction.
- Center_manifold wikiPageWikiLink Complex_amplitude.
- Center_manifold wikiPageWikiLink Delay_differential_equation.
- Center_manifold wikiPageWikiLink Dynamical_system.
- Center_manifold wikiPageWikiLink Eigenspace.
- Center_manifold wikiPageWikiLink Eigenvalues_and_eigenvectors.
- Center_manifold wikiPageWikiLink Eigenvectors.
- Center_manifold wikiPageWikiLink Equilibrium_point.
- Center_manifold wikiPageWikiLink Generalized_eigenvector.
- Center_manifold wikiPageWikiLink Hopf_bifurcation.
- Center_manifold wikiPageWikiLink Hyperbolic_equilibrium_point.
- Center_manifold wikiPageWikiLink Invariant_manifold.
- Center_manifold wikiPageWikiLink Invariant_subspace.
- Center_manifold wikiPageWikiLink Multiscale_mathematics.
- Center_manifold wikiPageWikiLink Multiscale_modeling.
- Center_manifold wikiPageWikiLink Normal_form_(mathematics).
- Center_manifold wikiPageWikiLink Phasor.
- Center_manifold wikiPageWikiLink Slow_manifold.
- Center_manifold wikiPageWikiLink Springer-Verlag.
- Center_manifold wikiPageWikiLink Springer_Science+Business_Media.
- Center_manifold wikiPageWikiLink Stable_manifold.
- Center_manifold wikiPageWikiLink Unstable_manifold.
- Center_manifold wikiPageWikiLink File:Saddle-node_phase_portrait_with_central_manifold.svg.
- Center_manifold wikiPageWikiLinkText "Center manifold".
- Center_manifold wikiPageWikiLinkText "center manifold".
- Center_manifold curator "Jack Carr".
- Center_manifold hasPhotoCollection Center_manifold.
- Center_manifold title "Center manifold".
- Center_manifold urlname "center_manifold".
- Center_manifold wikiPageUsesTemplate Template:Citation.
- Center_manifold wikiPageUsesTemplate Template:Scholarpedia.
- Center_manifold subject Category:Dynamical_systems.
- Center_manifold type Field.
- Center_manifold type Mechanic.
- Center_manifold type Physic.
- Center_manifold comment "In mathematics, the center manifold of an equilibrium point of a dynamical system consists of orbits whose behavior around the equilibrium point is not controlled by either the attraction of the stable manifold or the repulsion of the unstable manifold. The first step when studying equilibrium points of dynamical systems is to linearize the system. The eigenvectors corresponding to eigenvalues with negative real part form the stable eigenspace, which gives rise to the stable manifold.".
- Center_manifold label "Center manifold".
- Center_manifold sameAs Varietà_centrale.
- Center_manifold sameAs m.0b851q.
- Center_manifold sameAs Центральное_многообразие.
- Center_manifold sameAs Q4504202.
- Center_manifold sameAs Q4504202.
- Center_manifold wasDerivedFrom Center_manifold?oldid=663129198.
- Center_manifold depiction Saddle-node_phase_portrait_with_central_manifold.svg.
- Center_manifold isPrimaryTopicOf Center_manifold.