Shadowing and hyperbolicity for linear delay difference equations
Dynamical Systems
2024-12-10 v2
Abstract
It is known that hyperbolic linear delay difference equations are shadowable on the half-line. In this paper, we prove the converse and hence the equivalence between hyperbolicity and the positive shadowing property for the following two classes of linear delay difference equations: (a)~for nonautonomous equations with finite delays and uniformly bounded compact coefficient operators in (possibly infinite-dimensional) Banach spaces, (b)~for Volterra difference equations with infinite delay in finite dimensional spaces.
Cite
@article{arxiv.2401.10767,
title = {Shadowing and hyperbolicity for linear delay difference equations},
author = {Lucas Backes and Davor Dragicevic and Mihaly Pituk},
journal= {arXiv preprint arXiv:2401.10767},
year = {2024}
}
Comments
Revised version. Accepted for publication in Proceedings of the Royal Society of Edinburgh Section A: Mathematics