More Consequences of Hyperbolicity

  • Michael Shub

Abstract

Consider two submanifolds V and W of M which intersect at a point p. We say that V and W are transverse at p, V Ψ W, or that p is a point of transverse intersection of V and W, if
$${T_o}V + {T_o}W = {T_p}M$$
.

Keywords

Global Stability Unstable Manifold Unique Fixed Point Transverse Intersection Linear Automorphism 
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. [7.1]
    Hartman, P., Ordinary Differential Equations, 3rd edn, Birkhauser, Boston, 1983, 250.Google Scholar
  2. [7.2]
    Palais, R., Extending diffeomorphisms, Proc. Amer. Math. Soc. 11(1960), 274.MathSciNetMATHCrossRefGoogle Scholar
  3. [7.3]
    Palis, J., On the local structure of hyperbolic points in Banach space, An. Acad. Brasil. Ciênc. 40 (1968), 263.MathSciNetMATHGoogle Scholar
  4. [7.4]
    Pugh, C., On a theorem of P. Hartman, Amer. J. Math. 91 (1969), 363MathSciNetMATHCrossRefGoogle Scholar
  5. [7.5]
    Pugh, C. and Shub, M., Linearization of normally hyperbolic diffeomorphisms and flows, Invent. Math. 10 (1970), 187.MathSciNetMATHGoogle 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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