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Chow, Shui-Nee

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Author: Liu, Weishi × End date: 1999 × Start date: 1994 ×

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Center Manifolds for Invariant Sets

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

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.

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