About: Slow manifold

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In mathematics, the slow manifold of an equilibrium point of a dynamical system occurs as the most common example of a center manifold. One of the main methods of simplifying dynamical systems, is to reduce the dimension of the system to that of the slow manifold—center manifold theory rigorously justifies the modelling. For example, some global and regional models of the atmosphere or oceans resolve the so-called quasi-geostrophic flow dynamics on the slow manifold of the atmosphere/oceanic dynamics,and is thus crucial to forecasting with a climate model.

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rdfs:label	Slow manifold (en)
rdfs:comment	In mathematics, the slow manifold of an equilibrium point of a dynamical system occurs as the most common example of a center manifold. One of the main methods of simplifying dynamical systems, is to reduce the dimension of the system to that of the slow manifold—center manifold theory rigorously justifies the modelling. For example, some global and regional models of the atmosphere or oceans resolve the so-called quasi-geostrophic flow dynamics on the slow manifold of the atmosphere/oceanic dynamics,and is thus crucial to forecasting with a climate model. (en)
dcterms:subject	Dynamical systems
Wikipage page ID	25648887 (xsd:integer)
Wikipage revision ID	1106909113 (xsd:integer)
Link from a Wikipage to another Wikipage	Coordinate transform Dynamical system Invariant manifold Invariant subspace Robin boundary condition Mathematics Neumann boundary condition Ornstein–Uhlenbeck process Climate model Edward Norton Lorenz Eigenvalue Emergence Generalized eigenvector Equilibrium point Partial differential equation Center manifold Dirichlet boundary condition Dynamical systems Dynamical systems Bifurcation theory Ordinary differential equation Random walk Stochastic differential equation Quasi-geostrophic equations Geostrophic flow
sameAs	Slow manifold Slow manifold Slow manifold Slow manifold
dbp:wikiPageUsesTemplate	dbt:Reflist
has abstract	In mathematics, the slow manifold of an equilibrium point of a dynamical system occurs as the most common example of a center manifold. One of the main methods of simplifying dynamical systems, is to reduce the dimension of the system to that of the slow manifold—center manifold theory rigorously justifies the modelling. For example, some global and regional models of the atmosphere or oceans resolve the so-called quasi-geostrophic flow dynamics on the slow manifold of the atmosphere/oceanic dynamics,and is thus crucial to forecasting with a climate model. In some cases, a slow manifold is defined to be the invariant manifold on which the dynamics are slow compared to the dynamics off the manifold. The slow manifold in a particular problem would be a sub-manifold of either the stable, unstable, or center manifold, exclusively, that has the same dimension of, and is tangent to, the eigenspace with an associated eigenvalue (or eigenvalue pair) that has the smallest real part in magnitude. This generalizes the definition described in the first paragraph. Furthermore, one might define the slow manifold to be tangent to more than one eigenspace by choosing a cut-off point in an ordering of the real part eigenvalues in magnitude from least to greatest. In practice, one should be careful to see what definition the literature is suggesting. (en)
prov:wasDerivedFrom	wikipedia-en:Slow_manifold?oldid=1106909113&ns=0
page length (characters) of wiki page	10983 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Slow_manifold
is Link from a Wikipage to another Wikipage of	Environmental flow Method of averaging Inertial manifold Invariant manifold Edward Norton Lorenz Equation-free modeling Center manifold Stable manifold Multiple-scale analysis Multiscale modeling
is foaf:primaryTopic of	wikipedia-en:Slow_manifold

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