Stability of the Lyapunov exponents under perturbations

Abstract

For a linear-delay equation on an arbitrary Banach space, we describe a condition so that the Lyapunov exponents of the equation persist under sufficiently small linear as well as nonlinear perturbations. We consider both cases of discrete and continuous time with the study of delay-difference equations and delay equations, respectively. The delay can be any number from zero to infinity.