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- Inertial_manifold abstract "In mathematics, inertial manifolds are concerned with the long term behavior of the solutions of dissipative dynamical systems. Inertial manifolds are finite-dimensional, smooth, invariant manifolds that contain the global attractor and attract all solutions exponentially quickly. Since an inertial manifold is finite-dimensional even if the original system is infinite-dimensional, and because most of the dynamics for the system takes place on the inertial manifold, studying the dynamics on an inertial manifold produces a considerable simplification in the study of the dynamics of the original system.In many physical applications, inertial manifolds express an interaction law between the small and large wavelength structures. Some say that the small wavelengths are enslaved by the large (e.g. synergetics). Inertial manifolds may also appear as slow manifolds common in meteorology, or as the center manifold in any bifurcation. Computationally, numerical schemes for partial differential equations seek to capture the long term dynamics and so such numerical schemes form an approximate inertial manifold.".
- Inertial_manifold wikiPageExternalLink gencm.php.
- Inertial_manifold wikiPageID "37009413".
- Inertial_manifold wikiPageLength "9877".
- Inertial_manifold wikiPageOutDegree "18".
- Inertial_manifold wikiPageRevisionID "644570331".
- Inertial_manifold wikiPageWikiLink Attractor.
- Inertial_manifold wikiPageWikiLink Banach_space.
- Inertial_manifold wikiPageWikiLink Bifurcation_theory.
- Inertial_manifold wikiPageWikiLink Category:Dynamical_systems.
- Inertial_manifold wikiPageWikiLink Center_manifold.
- Inertial_manifold wikiPageWikiLink Dimension_(vector_space).
- Inertial_manifold wikiPageWikiLink Dissipation.
- Inertial_manifold wikiPageWikiLink Dynamical_system.
- Inertial_manifold wikiPageWikiLink Exponential_growth.
- Inertial_manifold wikiPageWikiLink Invariant_manifold.
- Inertial_manifold wikiPageWikiLink Manifold.
- Inertial_manifold wikiPageWikiLink Partial_differential_equation.
- Inertial_manifold wikiPageWikiLink Semigroup.
- Inertial_manifold wikiPageWikiLink Slow_manifold.
- Inertial_manifold wikiPageWikiLink State-transition_matrix.
- Inertial_manifold wikiPageWikiLink Synergetics_(Haken).
- Inertial_manifold wikiPageWikiLink Wandering_set.
- Inertial_manifold wikiPageWikiLinkText "inertial manifold".
- Inertial_manifold subject Category:Dynamical_systems.
- Inertial_manifold type Field.
- Inertial_manifold type Mechanic.
- Inertial_manifold type Physic.
- Inertial_manifold comment "In mathematics, inertial manifolds are concerned with the long term behavior of the solutions of dissipative dynamical systems. Inertial manifolds are finite-dimensional, smooth, invariant manifolds that contain the global attractor and attract all solutions exponentially quickly.".
- Inertial_manifold label "Inertial manifold".
- Inertial_manifold sameAs Q17098174.
- Inertial_manifold sameAs m.0n45lfq.
- Inertial_manifold sameAs Q17098174.
- Inertial_manifold wasDerivedFrom Inertial_manifold?oldid=644570331.
- Inertial_manifold isPrimaryTopicOf Inertial_manifold.