Advertisement

Stability and Genericity in Dynamical Systems

  • Steve Smale

Abstract

A general reference to this subject, with examples, written about the summer of 1967 is [7], (reported in a recent Bourbaki seminar by C. Godbillon). Here I will try to emphasize developments since. An important source of much of this more recent work should appear in the immediate future in [1].

Keywords

Zeta Function Periodic Point Stable Manifold Transversality Condition Stable Dynamical System 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Global Analysis, Proceedings of the 1968 AMS institute on global analysis at Berkeley. Vol. 1 (of 3 vols) is devoted to dynamical systems.Google Scholar
  2. [2]
    R. Bowen, Periodic points and measures for Axiom A diffeomorphisms, Trans. AMS 154 (1971), 377–397.MathSciNetMATHGoogle Scholar
  3. [3]
    R. Bowen, Markov partitions for Axiom A diffeomorphisms, Amer. J. Math. 92 (1970), 725–747.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    J. Guckenheimer, Axiom A + no cycles⇒ ζf(t) rational, Bull. AMS 76 (1970), 592–594.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    M. Hirsch, J. Pahs, C. Pugh, M. Shub, Neighborhoods of hyperbolic sets, Inventiones Math. 9 (1970), 121–134.MATHCrossRefGoogle Scholar
  6. [6]
    J. Pahs, On Morse-Smale dynamical systems, Topology 8 (1969), 385–405.CrossRefGoogle Scholar
  7. [7]
    S. Smale, Differentiable dynamical systems, Bull. AMS 73 (1967), 747–817.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1980

Authors and Affiliations

  • Steve Smale
    • 1
  1. 1.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA

Personalised recommendations