Center Manifolds for Invariant Sets

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Abstract:

We derive a general center manifolds theory for a class of compact invariant sets of flows generated by a smooth vector field in ℝn. By applying the Hadamard graph transform technique, it is shown that, associated to a natural dynamical characteristic 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. Copyright 2000 Academic Press.

Keywords: center manifold; graph transform; overflowing

Document Type: Research Article

Affiliations: 1: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia, 30332-0190 2: Department of Mathematics, University of Missouri–Columbia, Columbia, Missouri, 65211

Publication date: December 1, 2000

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