Diffeomorphisms with robustly ergodic shadowing (Q2874027)

Suppose that \(M\) is a closed \(C^\infty\) manifold. It is shown that, provided a mapping \(f\) is in the \(C^1\)-interior of the set of all diffeomorphims having the ergodic shadowing property, then \(f\) is structurally stable. Moreover, two further results on such diffeomorphisms are established: {\parindent=0.5cm\begin{itemize}\item[(1)] They satisfy Axiom A and the no-cycle condition (it has no \(k\)-cycles with \(k\geq 1\)). \item[(2)] If \(\Lambda_1,\Lambda_2\) are basic sets of \(f\) and \(p_1\in\Lambda_1\), \(p_2\in\Lambda_2\), then the corresponding stable/unstable manifolds satisfy \(W^s(p_1)\pitchfork W^u(p_2)\neq\emptyset\) and \(W^u(p_1)\pitchfork W^s(p_2)\neq\emptyset\).NEWLINENEWLINE\end{itemize}}