Invariant manifolds on non-linear operators

Type: Article

Publication Date: 1976-01-01

Citations: 71

DOI: https://doi.org/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 c o (E).The constructive nature of our proof has the advantage of ready adaptation to numerical methods.

Locations

  • Pacific Journal of Mathematics - View - PDF
  • Project Euclid (Cornell University) - View - PDF

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