Classical results concerning the asymptotic behavior solutions of systems of linear differential or difference equations lead to formulas containing factors that are asymptotically constant, i.e., k + o(1) as t tends to infinity. Here we are interested in more precise information about the o(1) terms, specifically how they depend precisely on certain perturbation terms in the equation. Results along these lines were given by Gel'fond and Kubenskaya for scalar difference equations and we will both extend and generalize one of them as well as provide some corresponding results for differential equations.
lowiial of Dkffeicrence Equnrions mid Applicatio~is iLiO!, Yai 7 , pp 03; -656 Repnnts nvailahle directly from the puhlichei Photocopy~ng permitted b) license only .; 2001 OPA iOverseas Publishers .Associ?rion) N V Pubiishd by iiicilse uniisi [he Gnriinr? snd RrcachOur purpose is to obtain conditions under which a kinematic similarity exists that reduces the linear difl'erence equation x(n+ 1) = A(n)x(n) to a linear equation with coefficient matrix B(n) being diagonal for sufficiently large n. It is shown that if A(n) is the sum of a bounded sequence A(n) plus a sequence P(n) --to as n-oo and if the omega-limit set of A (nj, in the associated skew-product flow, has full spectrum then such a kinematic similarity exists.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.