Weak shadowing for discrete dynamical systems on nonsmooth manifolds (Q1399356)

The author gives another proof of the result of \textit{R. M. Corless} and \textit{S. Yu. Pilyugin} [J. Math. Anal. Appl. 189, 409-423 (1995; Zbl 0821.58036)], which proved that weak shadowing is a \(C^{0}\) generic property in the space of discrete dynamical systems on a compact smooth manifold \(M\). The presented new proof does not assume that \(M\) has a differential structure and works even for systems on some compact metric spaces that are not manifold, such as a Hilbert cube and a Cantor set.