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单词 Invariant Manifold
释义

Invariant Manifold

When stable and unstable invariant Manifolds intersect, they do so in a Hyperbolic FixedPoint (Saddle Point). The invariantManifolds are then called Separatrices. A Hyperbolic Fixed Point is characterized by two ingoing stable Manifolds and two outgoingunstable Manifolds. In integrable systems, incoming and outgoing Manifoldsall join up smoothly.


A stable invariant Manifold of a Fixed Point is the set of all points such that the trajectory passingthrough tends to as .


An unstable invariant Manifold of a Fixed Point is the set of all points such that the trajectorypassing through tends to as .

See also Homoclinic Point
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更新时间:2025/2/22 5:13:46