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Erschienen in:
1982 | OriginalPaper | Buchkapitel
The Kupka-Smale Theorem
verfasst von : Jacob Palis Jr., Welington de Melo
Erschienen in: Geometric Theory of Dynamical Systems
Verlag: Springer US
Enthalten in: Professional Book Archive
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Let M be a compact manifold of dimension m and Xr(M) the space of Cr vector fields on M, r ≥ 1, with a Cr norm. In Chapter 2 we showed that the set G1 ⊂ Xr(M), consisting of fields whose singularities are hyperbolic, is open and dense in Xr(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 Xr(M). The original proof of the results dealt with here can be found in [44], [82] and [107].