Existence and persistence of invariant manifolds for semiflows in Banach space / Peter W. Bates, Kening Lu, Chongchun Zeng

Since the early 1970s, mathematicians have tried to extend the work of N.Fenichel and M.Hirsch, C.Pugh and M.Shub to give conditions under which invariant manifolds for semi-flows 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.