Memoirs of the American Mathematical Society 1998; 129 pp; softcover Volume: 135 ISBN10: 0821808680 ISBN13: 9780821808689 List Price: US$50 Individual Members: US$30 Institutional Members: US$40 Order Code: MEMO/135/645
 Since the early 1970s, mathematicians have tried to extend the work of N. Fenichel and of M. Hirsch, C. Pugh and M. Shub to give conditions under which invariant manifolds for semiflows persist under perturbation of the semiflow. This work provides natural conditions and establishes the desired theorem. The technique is geometric in nature, and in addition to rigorous proofs, an informal outline of the approach is given with useful illustrations. Features:  Important theoretical tools for working with infinitedimensional dynamical systems, such as PDEs.
 Previously unpublished results.
 New ideas regarding invariant manifolds.
Readership Graduate students, research mathematicians, physicists, and engineers working in analysis, applied mathematics, physical sciences and engineering. Table of Contents  Introduction
 Notation and preliminaries
 Statements of theorems
 Local coordinate systems
 Cone lemmas
 Centerunstable manifold
 Centerstable manifold
 Smoothness of centerstable manifold
 Smoothness of centerunstable manifold
 Persistence of invariant manifold
 Persistence of normal hyperbolicity
 Invariant manifolds for perturbed semiflow
 References
