Center manifolds for invariant sets

We derive a general center manifolds theory for a class of compact invarian t sets of flows generated by a smooth vector field in R-n. By applying the Hadamard graph transform technique, it is shown that, associated to a natur al dynamical characteristic of the linearized now along the invariant set, there exists an invariant manifold (called a center manifold) of the invari ant set which contains every locally bounded solution (in particular, conta ins the invariant set) and is persistent under small perturbations. (C) 200 0 Academic Press.