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In mathematics, especially in the study of dynamical systems and differential equations, the stable manifold theorem is an important result about the structure of the set of orbits approaching a given hyperbolic fixed point. It roughly states that the existence of a local diffeomorphism near a fixed point implies the existence of a local stable center manifold containing that fixed point. This manifold has dimension equal to the number of eigenvalues of the Jacobian matrix of the fixed point that are less than 1.

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  • Stable manifold theorem
  • 穩定流形定理
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  • 穩定流形定理（stable manifold theorem）是數學定理，动力系统及微分方程有關，是有關趨近給定的集合之結構。 令 為光滑函数，存在雙曲不動點。令為的穩定流形，則為不穩定流形。 定理提到 * 為光滑流形，且切空间也和在點線性化的穩定空間（stable space）有相同維度。 * 為光滑流形，且切空间也和在點線性化的不穩定空間（unstable space）有相同維度。 因此是穩定流形，而是不穩定流形。
  • In mathematics, especially in the study of dynamical systems and differential equations, the stable manifold theorem is an important result about the structure of the set of orbits approaching a given hyperbolic fixed point. It roughly states that the existence of a local diffeomorphism near a fixed point implies the existence of a local stable center manifold containing that fixed point. This manifold has dimension equal to the number of eigenvalues of the Jacobian matrix of the fixed point that are less than 1.
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  • 穩定流形定理（stable manifold theorem）是數學定理，动力系统及微分方程有關，是有關趨近給定的集合之結構。 令 為光滑函数，存在雙曲不動點。令為的穩定流形，則為不穩定流形。 定理提到 * 為光滑流形，且切空间也和在點線性化的穩定空間（stable space）有相同維度。 * 為光滑流形，且切空间也和在點線性化的不穩定空間（unstable space）有相同維度。 因此是穩定流形，而是不穩定流形。
  • In mathematics, especially in the study of dynamical systems and differential equations, the stable manifold theorem is an important result about the structure of the set of orbits approaching a given hyperbolic fixed point. It roughly states that the existence of a local diffeomorphism near a fixed point implies the existence of a local stable center manifold containing that fixed point. This manifold has dimension equal to the number of eigenvalues of the Jacobian matrix of the fixed point that are less than 1.
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  • StableManifoldTheorem
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  • StableManifoldTheorem
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