Stable Manifold Theorem
Let
be a smooth map with hyperbolic fixed point at p. We denote by the stable set and by the unstable set of p.
The theorem states that
- is a smooth manifold and its tangent space has the same dimension as the stable space of the linearization of f at p.
- is a smooth manifold and its tangent space has the same dimension as the unstable space of the linearization of f at p.
Accordingly is a stable manifold and is an unstable manifold.
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