Year: 2021
Type: preprint
Abstract: In this paper we examine the interplay between recurrence properties and the shadowing property in dynamical systems on compact metric spaces. In particular, we demonstrate that if the dynamical system $(X,f)$ has shadowing, then it is recurrent if and only if it is minimal. Furthermore, we show that a uniformly rigid system $(X,f)$ has shadowing if and only if $X$ is totally disconnected and use this to demonstrate the existence of a space $X$ for which no surjective system $(X,f)$ has shadowing. We further refine these results to discuss the dynamics that can occur in spaces with compact space of self-maps.
Source: arXiv (Cornell University)
Author: Meddaugh, Jonathan
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3214912784