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In dynamical systems, a branch of mathematics, an invariant manifold is a topological manifold that is invariant under the action of the dynamical system.[1] Examples include the slow manifold, center manifold, stable manifold, unstable manifold, subcenter manifold and inertial manifold.
Typically, although by no means always, invariant manifolds are constructed as a 'perturbation' of an invariant subspace about an equilibrium.
In dissipative systems, an invariant manifold based upon the gravest, longest lasting modes forms an effective low-dimensional, reduced, model of the dynamics.[2]
^Hirsh M.W., Pugh C.C., Shub M., Invariant Manifolds, Lect. Notes. Math., 583, Springer, Berlin — Heidelberg, 1977
^A. J. Roberts. The utility of an invariant manifold description of the evolution of a dynamical system. SIAM J. Math. Anal., 20:1447–1458, 1989. http://locus.siam.org/SIMA/volume-20/art_0520094.html Archived 2008-08-20 at the Wayback Machine
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respectively. Invariantmanifold Center manifold Limit set Julia set Slow manifold Inertial manifold Normally hyperbolic invariantmanifold Lagrangian coherent...
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