Stability and Genericity in Dynamical Systems

  • Steve Smale


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].


Zeta Function Periodic Point Stable Manifold Transversality Condition Stable Dynamical System 
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  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

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