Shadowing, Hyers--Ulam stability and hyperbolicity for nonautonomous linear delay differential equations
Dynamical Systems
2024-03-20 v1
Abstract
It is known that hyperbolic non\-autonomous linear delay differential equations in a finite dimensional space are Hyers--Ulam stable and hence shadowable. The converse result is available only in the special case of autonomous and periodic linear delay differential equations with a simple spectrum. In this paper, we prove the converse and hence the equivalence of all three notions in the title for a general class of nonautonomous linear delay differential equations with uniformly bounded coefficients. The importance of the boundedness assumption is shown by an example.
Cite
@article{arxiv.2401.10764,
title = {Shadowing, Hyers--Ulam stability and hyperbolicity for nonautonomous linear delay differential equations},
author = {Lucas Backes and Davor Dragicevic and Mihaly Pituk},
journal= {arXiv preprint arXiv:2401.10764},
year = {2024}
}