Vol. 96, No. 1, 1981

Recent Issues
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Invariant manifolds for regular points

Jorge Lewowicz

Vol. 96 (1981), No. 1, 163–173
Abstract

In this article we prove, for a differentiable vector field or a diffeomorphism on a smooth manifold, that the set of points such that the semitrajectories issuing from them approach a particular semitrajectory at a given exponential rate, constitute a differentiable submanifold, provided the differential of the flow has a certain similar behavior on that trajectory. (See Theorem 1 below, for a precise statement). In particular, the stable manifold theorem for hyperbolic sets ([3], [6, XI]) follows as a corollary.

Although we only consider the C1-case, the same methods, which are essentially classical ([2, Ch. XIII]), could be applied to obtain higher differentiability properties.

Since I have not seen in the literature this type of results for points which are neither equilibrium nor periodic points, and on account of [6, XI–8], I thought that their publication might not be entirely devoid of interest.

Mathematical Subject Classification
Primary: 58F15
Secondary: 58F10
Milestones
Published: 1 September 1981
Authors
Jorge Lewowicz