Bi-shadowing and delay equations

Abstract

Bi-shadowing is an extension to the concept of shadowing and is usually used in the context of comparing computed trajectories with the true trajectories of a dynamical system in Rn. Here the concept is defined in a Banach space and is applied to delay equations to give an apparently new result on nonlinear perturbations of linear delay equations. This is essentially a form of robustness with respect to small nonlinear disturbances.