Invariant manifolds on non-linear operators

John Campbell Wells

Vol. 62 (1976), No. 1, 285–293

DOI: 10.2140/pjm.1976.62.285

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

Mathematical Subject Classification

Primary: 58F10

Secondary: 34G05

Milestones

Received: 23 May 1975

Published: 1 January 1976