Stable Manifolds

  • Michael Shub
Chapter

Abstract

We have begun to study hyperbolic invariant sets. Before we continue we must generalize our definitions in the case of a fixed point, to allow us to work in an arbitrary Banach space.

Keywords

Banach Space Lipschitz Function Global Stability Unstable Manifold Stable Manifold 
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References

  1. [5.1]
    Hirsch, M. W., Pugh, C. C. and Shub, M., Invariant Manifolds, Lecture Notes in Mathematics, No. 583, Springer-Verlag, New York, 1976.Google Scholar
  2. [5.2]
    Irwin, M. C., On the stable manifold theorem, Bull. London Math. Soc. 2 (1970), 196.MathSciNetMATHCrossRefGoogle Scholar
  3. [5.3]
    Irwin, M. C., On the smoothness of the composition map, Quart. J. Math. Oxford 23 (1972), 113MathSciNetMATHCrossRefGoogle Scholar
  4. Irwin, M. C., On the smoothness of the composition map, Bull. London Math. Soc. 2 (1970), 196.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Michael Shub
    • 1
  1. 1.Thomas J. Watson Research CenterIBMYorktown HeightsUSA

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