The Kupka-Smale Theorem

Jacob Palis and Welington de Melo
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Jacob Palis: Instituto de Matemática Pura e Aplicada
Welington de Melo: Instituto de Matemática Pura e Aplicada

Chapter Chapter 3 in Geometric Theory of Dynamical Systems, 1982, pp 91-114 from Springer

Abstract: 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].

Keywords: Vector Field; Periodic Point; Invariant Manifold; Compact Manifold; Unstable Manifold (search for similar items in EconPapers)
Date: 1982
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DOI: 10.1007/978-1-4612-5703-5_3

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