Orbital shadowing and stability for vector fields

The orbital shadowing property means that there exists a true orbit close to the approximate orbit in the sense of Hausdroff distance. In this paper, we show that in any dimension the C-1 interior of the set of vector fields having the orbital shadowing property is contained in the set of Omega-stable vector fields. We also discuss the structural stability of vector fields having the orbital shadowing property. (C) 2020 Elsevier Inc. All rights reserved.