Vol. 62, No. 1, 1976

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Invariant manifolds on non-linear operators

John Campbell Wells

Vol. 62 (1976), No. 1, 285–293

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 c0(E). The constructive nature of our proof has the advantage of ready adaptation to numerical methods.

Mathematical Subject Classification
Primary: 58F10
Secondary: 34G05
Received: 23 May 1975
Published: 1 January 1976
John Campbell Wells