Invariant manifold

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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]