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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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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