Center Manifolds for Invariant Sets

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. © 2000 Academic Press.