Differentiable maps having hyperbolic sets (Q1379773)

In [\textit{S. Newhouse} and \textit{J. Palis}, Astérisque 31, 44-140 (1976; Zbl 0322.58009)] it was shown that the set of all \(C^r\)-diffeomorphisms satisfying both Axiom A and the strong transversality of a closed \(C^{\infty}\)-manifold is \(C^r\)-open in the set of all \(C^r\)-diffeomorphisms (\(r\geq 1\)). The authors have studied the problem for differentiable mappings. \textit{K. Sakai} [Topology Appl. 54, No. 1-3, 173-182 (1993; Zbl 0797.58044)], proved that the set of all \(C^r\)-regular maps satisfying Axiom A and the strong transversality is open in the set of \(C^r\)-differentiable maps with the \(C^r\)-topology. In the present article, the authors prove the result for the set of all \(C^r\)-differentiable maps satisfying both Axiom A and strong transversality.