An arbitrary diffeomorphism \(f\) of class \(C^{1}\) acting from an open subset \(U\) of Riemannian manifold \(M\) of dimension \(m,\) \(m\geqslant 2,\) into \(f(U)\subset M\) is considered.Let \(A\) be a compact subset of \(U\) invariant for \(f,\) i. e., \(f(A)=A.\) Various sufficient conditions are proposed under which \(A\) is a hyperbolic set of the diffeomorphism \(f.\)
