stable manifold theorem
Let be an open subset of containing the origin, let , and let be the flow of the nonlinear system .
Suppose that and that has eigenvalues with negative real part and eigenvalues with positive real part. Then there exists a -dimensional differentiable manifold tangent to the stable subspace of the linear system at such that for all , and for all ,
and there exists an dimensional differentiable manifold tangent to the unstable subspace of at such that for all , and for all ,
Title | stable manifold theorem |
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Canonical name | StableManifoldTheorem |
Date of creation | 2013-03-22 12:57:17 |
Last modified on | 2013-03-22 12:57:17 |
Owner | jarino (552) |
Last modified by | jarino (552) |
Numerical id | 4 |
Author | jarino (552) |
Entry type | Theorem |
Classification | msc 34C99 |