Shadowing as a Structural Property of the Space of Dynamical Systems

TL;DR

This paper characterizes the shadowing property as a structural feature of the space of dynamical systems on certain compact metric spaces, simplifying the verification process for shadowing.

Contribution

It introduces a new structural perspective on shadowing and shows that pseudo-orbit shadowing suffices to determine shadowing in these spaces.

Findings

Shadowing is a structural property in certain compact metric spaces.

Pseudo-orbit shadowing is sufficient to verify shadowing.

The characterization simplifies analysis of dynamical systems.

Abstract

We demonstrate that there is a large class of compact metric spaces for which the shadowing property can be characterized as a structural property of the space of dynamical systems. We also demonstrate for this class of spaces, that in order to determine whether a system has shadowing, it is sufficient to check that continuously generated pseudo-orbits can be shadowed.