Theory of pseudo-orbit shadowing in dynamical systems (Q416843)

The paper is a survey on recent advances on shadowing theory for homeomorphisms (and flows) acting on metric spaces. Main topics considered in the survey are: {\parindent=8mm \begin{itemize}\item[(i)] various definitions of the shadowing property (e.g. periodic shadowing, limit shadowing, Lipschitz shadowing, etc.) and relations between them; \item[(ii)] \(C^1\) interior of various classes (i.e. maps with different types of shadowing property) in the space of \(C^1\)-diffeomorphisms on a manifold; \item[(iii)] shadowing properties equivalent to structural stability for diffeomorphisms on manifolds; \item[(iv)] cases when shadowing is (or is not) generic in \(C^0\) or \(C^1\) topology in the space, respectively, of homeomorphisms and diffeomorphisms on a manifold. \end{itemize}}