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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. The behavior on the center manifold is generally not determined by the linearization and thus more difficult to study.Center manifolds play an important role in bifurcation theory because interesting behavior takes place on the 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 wikiPageRevisionID "599074043".
- Center_manifold curator "Jack Carr".
- Center_manifold hasPhotoCollection Center_manifold.
- Center_manifold title "Center manifold".
- Center_manifold urlname "center_manifold".
- Center_manifold subject Category:Dynamical_systems.
- Center_manifold type Abstraction100002137.
- Center_manifold type Attribute100024264.
- Center_manifold type DynamicalSystem106246361.
- Center_manifold type DynamicalSystems.
- Center_manifold type PhaseSpace100029114.
- Center_manifold type Space100028651.
- 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 label "Центральное многообразие".
- Center_manifold sameAs m.0b851q.
- Center_manifold sameAs Q4504202.
- Center_manifold sameAs Q4504202.
- Center_manifold sameAs Center_manifold.
- Center_manifold wasDerivedFrom Center_manifold?oldid=599074043.
- Center_manifold depiction Saddle-node_phase_portrait_with_central_manifold.svg.
- Center_manifold isPrimaryTopicOf Center_manifold.
