Exponential dichotomy for almost periodic linear difference equations. (English) Zbl 0687.39002
Suppose that A(n) is an almost periodic matrix function of the integer variable n, that A(n) is invertible for each \(n\in Z\) and that \(A^{- 1}(n)\) is bounded on Z. Then it is proved that if the linear difference equation \(x(n+1)=A(n)\times (n)\) has an exponential dichotomy on a set \(\{m,m+1,...,m+T\}\) of consecutive integers with T sufficiently large, then it has an exponential dichotomy on all of Z. The results obtained are discrete analogues of the corresponding results of K. J. Palmer [Proc. Am. Math. Soc. 101, 293-298 (1987; Zbl 0664.34016)].
Reviewer: B.Aulbach