Invariant manifolds on non-linear operators

Abstract

In this paper we generalize the classical stable manifold theorem at a point as well as a recent result of M. Hirsch, C. Pugh and M. Shub. We deduce the existence of the invariant manifolds, their smoothness and their continuity under small perturbations of the underlying endomorphism entirely from the inverse function theorem and an easy proposition about smoothness of maps on c o (E).