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The Kupka-Smale Theorem

In: Geometric Theory of Dynamical Systems

Author

Listed:
  • Jacob Palis Jr.

    (Instituto de Matemática Pura e Aplicada)

  • Welington de Melo

    (Instituto de Matemática Pura e Aplicada)

Abstract

Let M be a compact manifold of dimension m and X r (M) the space of C r vector fields on M, r ≥ 1, with a C r norm. In Chapter 2 we showed that the set G1 ⊂ X r (M), consisting of fields whose singularities are hyperbolic, is open and dense in X r (M). This is an example of a generic property, i.e. a property that is satisfied by almost all vector fields. In this chapter we shall analyse other generic properties in X r (M). The original proof of the results dealt with here can be found in [44], [82] and [107].

Suggested Citation

  • Jacob Palis Jr. & Welington de Melo, 1982. "The Kupka-Smale Theorem," Springer Books, in: Geometric Theory of Dynamical Systems, chapter 0, pages 91-114, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-5703-5_3
    DOI: 10.1007/978-1-4612-5703-5_3
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