Center manifolds for smooth invariant manifolds

Chow, Shui-Nee; Liu, Weishi; Yi, Yingfei

doi:10.1090/S0002-9947-00-02443-0

Center manifolds for smooth invariant manifolds
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Trans. Amer. Math. Soc. 352 (2000), 5179-5211 Request permission

Abstract:

We study dynamics of flows generated by smooth vector fields in ${\mathbb {R}}^n$ in the vicinity of an invariant and closed smooth manifold $Y$. By applying the Hadamard graph transform technique, we show that there exists an invariant manifold (called a center manifold of $Y$) based on the information of the linearization along $Y$, which contains every locally bounded solution and is persistent under small perturbations.

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