Let M be a smooth compact manifold, and f: MM a diffeomorphism. Our goal is to study the structure of the orbits of f, where the orbit of a point x is the set {f n(x)|n ∈ Z}. We seek to describe the “history” of points of M; i.e., to follow them as we repeat f many times. First, the points with the simplest histories.


Periodic Point Global Stability Baire Property Vector Field Versus Closing Lemma 
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© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

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

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