Differentiable maps having the uniformly shadowing property (Q1612264)

(1) If a \(C^r\), \(r \geq 1\), differentiable map \(f\) on a closed and \(C^\infty\) manifold satisfies Axiom A and the strong transversality condition then the inverse limit system \(\widehat{f}\) has the \(C^r\) uniformly shadowing property. (2) If a \(C^1\) map satisfies Axiom A, then \(C^1\) uniformly shadowing property is equivalent to the strong transversality condition.