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Chow, Shui-Nee

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    Center Manifolds for Invariant Sets
    (Georgia Institute of Technology, 1999) Chow, Shui-Nee ; Liu, Weishi ; Yi, Yingfei
    We derive a general center manifolds theory for a class of compact invariant sets of flows generated by a smooth vector fields in R^n. By applying the Hadamard graph transform technique, it is shown that, associated to certain dynamical characteristics of the linearized flow along the invariant set, there exists an invariant manifold (called a center manifold) of the invariant set which contains every locally bounded solution (in particular, contains the invariant set) and is persistent under small perturbations.
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    Center Manifolds for Invariant Manifolds
    (Georgia Institute of Technology, 1997) Chow, Shui-Nee ; Liu, Weishi ; Yi, Yingfei
    We study dynamics of flows generated from smooth vector fields in 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.