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Abstract

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.

Keywords

Periodic Point Global Stability Baire Property Vector Field Versus Closing Lemma 
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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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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