\(C^ r\) Axiom A maps having strong transversality. (English) Zbl 0797.58044
Denote by \(R^ r(M)\) the set of all \(C^ r\) regular maps of a closed \(C^ \infty\) manifold \(M\). The author shows that the set of all \(f \in R^ r(M)\) (\(r \geq 1\)), satisfying Axiom A and strong transversality, is open in \(R^ r(M)\). This is a generalization of the result by Newhouse and Palis for \(C^ r\) diffeomorphisms.
Reviewer: Yu.E.Gliklikh (Voronezh)
MSC:
37C75 | Stability theory for smooth dynamical systems |
37D99 | Dynamical systems with hyperbolic behavior |
References:
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